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1,501
What's a real-world example of "overfitting"?
This one is made-up, but I hope it will illustrate the case. Example 1 First, let's make up some random data. Here you have $k=100$ variables, each drawn from a standard normal distribution, with $n=100$ cases: set.seed(123) k <- 100 data <- replicate(k, rnorm(100)) colnames(data) <- make.names(1:k) data <- as.data.fra...
What's a real-world example of "overfitting"?
This one is made-up, but I hope it will illustrate the case. Example 1 First, let's make up some random data. Here you have $k=100$ variables, each drawn from a standard normal distribution, with $n=1
What's a real-world example of "overfitting"? This one is made-up, but I hope it will illustrate the case. Example 1 First, let's make up some random data. Here you have $k=100$ variables, each drawn from a standard normal distribution, with $n=100$ cases: set.seed(123) k <- 100 data <- replicate(k, rnorm(100)) colname...
What's a real-world example of "overfitting"? This one is made-up, but I hope it will illustrate the case. Example 1 First, let's make up some random data. Here you have $k=100$ variables, each drawn from a standard normal distribution, with $n=1
1,502
What's a real-world example of "overfitting"?
A common problem that results in overfitting in real life is that in addition to terms for a correctly specified model, we may have have added something extraneous: irrelevant powers (or other transformations) of the correct terms, irrelevant variables, or irrelevant interactions. This happens in multiple regression if...
What's a real-world example of "overfitting"?
A common problem that results in overfitting in real life is that in addition to terms for a correctly specified model, we may have have added something extraneous: irrelevant powers (or other transfo
What's a real-world example of "overfitting"? A common problem that results in overfitting in real life is that in addition to terms for a correctly specified model, we may have have added something extraneous: irrelevant powers (or other transformations) of the correct terms, irrelevant variables, or irrelevant intera...
What's a real-world example of "overfitting"? A common problem that results in overfitting in real life is that in addition to terms for a correctly specified model, we may have have added something extraneous: irrelevant powers (or other transfo
1,503
What's a real-world example of "overfitting"?
A form of overfitting is fairly common in sports, namely to identify patterns to explain past results by factors that have no or at best vague power to predict future results. A common feature of these "patterns" is that they are often based on very few cases so that pure chance is probably the most plausible explanati...
What's a real-world example of "overfitting"?
A form of overfitting is fairly common in sports, namely to identify patterns to explain past results by factors that have no or at best vague power to predict future results. A common feature of thes
What's a real-world example of "overfitting"? A form of overfitting is fairly common in sports, namely to identify patterns to explain past results by factors that have no or at best vague power to predict future results. A common feature of these "patterns" is that they are often based on very few cases so that pure c...
What's a real-world example of "overfitting"? A form of overfitting is fairly common in sports, namely to identify patterns to explain past results by factors that have no or at best vague power to predict future results. A common feature of thes
1,504
What's a real-world example of "overfitting"?
When I was trying to understand this myself, I started thinking in terms of analogies with describing real objects, so I guess it's as "real world" as you can get, if you want to understand the general idea: Say you want to describe to someone the concept of a chair, so that they get a conceptual model that allows them...
What's a real-world example of "overfitting"?
When I was trying to understand this myself, I started thinking in terms of analogies with describing real objects, so I guess it's as "real world" as you can get, if you want to understand the genera
What's a real-world example of "overfitting"? When I was trying to understand this myself, I started thinking in terms of analogies with describing real objects, so I guess it's as "real world" as you can get, if you want to understand the general idea: Say you want to describe to someone the concept of a chair, so tha...
What's a real-world example of "overfitting"? When I was trying to understand this myself, I started thinking in terms of analogies with describing real objects, so I guess it's as "real world" as you can get, if you want to understand the genera
1,505
What's a real-world example of "overfitting"?
In predictive modeling, the idea is to use the data at hand to discover the trends that exist and that can be generalized to future data. By including variables in your model that have some minor, non-significant effect you are abandoning this idea. What you are doing is considering the specific trends in your specific...
What's a real-world example of "overfitting"?
In predictive modeling, the idea is to use the data at hand to discover the trends that exist and that can be generalized to future data. By including variables in your model that have some minor, non
What's a real-world example of "overfitting"? In predictive modeling, the idea is to use the data at hand to discover the trends that exist and that can be generalized to future data. By including variables in your model that have some minor, non-significant effect you are abandoning this idea. What you are doing is co...
What's a real-world example of "overfitting"? In predictive modeling, the idea is to use the data at hand to discover the trends that exist and that can be generalized to future data. By including variables in your model that have some minor, non
1,506
What's a real-world example of "overfitting"?
Here is a "real world" example not in the sense that somebody happened to come across it in research, but in the sense that it uses everyday concepts without many statistic-specific terms. Maybe this way of saying it will be more helpful for some people whose training is in other fields. Imagine that you have a databa...
What's a real-world example of "overfitting"?
Here is a "real world" example not in the sense that somebody happened to come across it in research, but in the sense that it uses everyday concepts without many statistic-specific terms. Maybe this
What's a real-world example of "overfitting"? Here is a "real world" example not in the sense that somebody happened to come across it in research, but in the sense that it uses everyday concepts without many statistic-specific terms. Maybe this way of saying it will be more helpful for some people whose training is in...
What's a real-world example of "overfitting"? Here is a "real world" example not in the sense that somebody happened to come across it in research, but in the sense that it uses everyday concepts without many statistic-specific terms. Maybe this
1,507
What's a real-world example of "overfitting"?
Here's a real-life example of overfitting that I helped perpetrate and then tried (unsuccessfully) to avert: I had several thousand independent, bivariate time series, each with no more than 50 data points, and the modeling project involved fitting a vector autoregression (VAR) to each one. No attempt was made to regul...
What's a real-world example of "overfitting"?
Here's a real-life example of overfitting that I helped perpetrate and then tried (unsuccessfully) to avert: I had several thousand independent, bivariate time series, each with no more than 50 data p
What's a real-world example of "overfitting"? Here's a real-life example of overfitting that I helped perpetrate and then tried (unsuccessfully) to avert: I had several thousand independent, bivariate time series, each with no more than 50 data points, and the modeling project involved fitting a vector autoregression (...
What's a real-world example of "overfitting"? Here's a real-life example of overfitting that I helped perpetrate and then tried (unsuccessfully) to avert: I had several thousand independent, bivariate time series, each with no more than 50 data p
1,508
What's a real-world example of "overfitting"?
My favourite is the β€œ3964 formula” discovered before the World Cup soccer competition in 1998: Brazil won the championships in 1970 and 1994. Sum up these 2 numbers and you will get 3964; Germany won in 1974 and 1990, adding up again to 3964; the same thing with Argentina winning in 1978 and 1986 (1978+1986 = 3964). ...
What's a real-world example of "overfitting"?
My favourite is the β€œ3964 formula” discovered before the World Cup soccer competition in 1998: Brazil won the championships in 1970 and 1994. Sum up these 2 numbers and you will get 3964; Germany wo
What's a real-world example of "overfitting"? My favourite is the β€œ3964 formula” discovered before the World Cup soccer competition in 1998: Brazil won the championships in 1970 and 1994. Sum up these 2 numbers and you will get 3964; Germany won in 1974 and 1990, adding up again to 3964; the same thing with Argentina...
What's a real-world example of "overfitting"? My favourite is the β€œ3964 formula” discovered before the World Cup soccer competition in 1998: Brazil won the championships in 1970 and 1994. Sum up these 2 numbers and you will get 3964; Germany wo
1,509
What's a real-world example of "overfitting"?
Studying for an exam by memorising the answers to last year's exam.
What's a real-world example of "overfitting"?
Studying for an exam by memorising the answers to last year's exam.
What's a real-world example of "overfitting"? Studying for an exam by memorising the answers to last year's exam.
What's a real-world example of "overfitting"? Studying for an exam by memorising the answers to last year's exam.
1,510
What's a real-world example of "overfitting"?
Many intelligent people in this thread --- many much more versed in statistics than I am. But I still don't see an easy-to-understand to the lay-person example. The Presidential example doesn't quite hit the bill in terms of typical overfitting, because while it is technically overfitting in each one of its wild claims...
What's a real-world example of "overfitting"?
Many intelligent people in this thread --- many much more versed in statistics than I am. But I still don't see an easy-to-understand to the lay-person example. The Presidential example doesn't quite
What's a real-world example of "overfitting"? Many intelligent people in this thread --- many much more versed in statistics than I am. But I still don't see an easy-to-understand to the lay-person example. The Presidential example doesn't quite hit the bill in terms of typical overfitting, because while it is technica...
What's a real-world example of "overfitting"? Many intelligent people in this thread --- many much more versed in statistics than I am. But I still don't see an easy-to-understand to the lay-person example. The Presidential example doesn't quite
1,511
What's a real-world example of "overfitting"?
Most optimization methods have some fudge factors aka hyperparameters. A real example: For all systems under study, the following parameters yielded a fast and robust behavior: $N_{min} = 5,\ \ f_{inc} = 1.1,\ \ f_{dec} = 0.5,\ \ \alpha_{start} = 0.1, \ \ f_{\alpha} = 0.99.$ Is this over fitting, or just fitting ...
What's a real-world example of "overfitting"?
Most optimization methods have some fudge factors aka hyperparameters. A real example: For all systems under study, the following parameters yielded a fast and robust behavior: $N_{min} = 5,\ \ f_{
What's a real-world example of "overfitting"? Most optimization methods have some fudge factors aka hyperparameters. A real example: For all systems under study, the following parameters yielded a fast and robust behavior: $N_{min} = 5,\ \ f_{inc} = 1.1,\ \ f_{dec} = 0.5,\ \ \alpha_{start} = 0.1, \ \ f_{\alpha} = 0....
What's a real-world example of "overfitting"? Most optimization methods have some fudge factors aka hyperparameters. A real example: For all systems under study, the following parameters yielded a fast and robust behavior: $N_{min} = 5,\ \ f_{
1,512
What's a real-world example of "overfitting"?
A bit intuitive, but maybe it'll help. Let's say you want to learn some new language. How do you learn? instead of learning the rules in a course, you use examples. Specifically, TV shows. So you like crime shows, and you watch few series of some cop show. Then, you take another crime show and watch some series form th...
What's a real-world example of "overfitting"?
A bit intuitive, but maybe it'll help. Let's say you want to learn some new language. How do you learn? instead of learning the rules in a course, you use examples. Specifically, TV shows. So you like
What's a real-world example of "overfitting"? A bit intuitive, but maybe it'll help. Let's say you want to learn some new language. How do you learn? instead of learning the rules in a course, you use examples. Specifically, TV shows. So you like crime shows, and you watch few series of some cop show. Then, you take an...
What's a real-world example of "overfitting"? A bit intuitive, but maybe it'll help. Let's say you want to learn some new language. How do you learn? instead of learning the rules in a course, you use examples. Specifically, TV shows. So you like
1,513
How does the reparameterization trick for VAEs work and why is it important?
After reading through Kingma's NIPS 2015 workshop slides, I realized that we need the reparameterization trick in order to backpropagate through a random node. Intuitively, in its original form, VAEs sample from a random node $z$ which is approximated by the parametric model $q(z \mid \phi, x)$ of the true posterior. B...
How does the reparameterization trick for VAEs work and why is it important?
After reading through Kingma's NIPS 2015 workshop slides, I realized that we need the reparameterization trick in order to backpropagate through a random node. Intuitively, in its original form, VAEs
How does the reparameterization trick for VAEs work and why is it important? After reading through Kingma's NIPS 2015 workshop slides, I realized that we need the reparameterization trick in order to backpropagate through a random node. Intuitively, in its original form, VAEs sample from a random node $z$ which is appr...
How does the reparameterization trick for VAEs work and why is it important? After reading through Kingma's NIPS 2015 workshop slides, I realized that we need the reparameterization trick in order to backpropagate through a random node. Intuitively, in its original form, VAEs
1,514
How does the reparameterization trick for VAEs work and why is it important?
Assume we have a normal distribution $q$ that is parameterized by $\theta$, specifically $q_{\theta}(x) = N(\theta,1)$. We want to solve the below problem $$ \text{min}_{\theta} \quad E_q[x^2] $$ This is of course a rather silly problem and the optimal $\theta$ is obvious. However, here we just want to understand how t...
How does the reparameterization trick for VAEs work and why is it important?
Assume we have a normal distribution $q$ that is parameterized by $\theta$, specifically $q_{\theta}(x) = N(\theta,1)$. We want to solve the below problem $$ \text{min}_{\theta} \quad E_q[x^2] $$ This
How does the reparameterization trick for VAEs work and why is it important? Assume we have a normal distribution $q$ that is parameterized by $\theta$, specifically $q_{\theta}(x) = N(\theta,1)$. We want to solve the below problem $$ \text{min}_{\theta} \quad E_q[x^2] $$ This is of course a rather silly problem and th...
How does the reparameterization trick for VAEs work and why is it important? Assume we have a normal distribution $q$ that is parameterized by $\theta$, specifically $q_{\theta}(x) = N(\theta,1)$. We want to solve the below problem $$ \text{min}_{\theta} \quad E_q[x^2] $$ This
1,515
How does the reparameterization trick for VAEs work and why is it important?
A reasonable example of the mathematics of the "reparameterization trick" is given in goker's answer, but some motivation could be helpful. (I don't have permissions to comment on that answer; thus here is a separate answer.) In short, we want to compute some value $G_\theta$ of the form, $$G_\theta = \nabla_{\theta}E_...
How does the reparameterization trick for VAEs work and why is it important?
A reasonable example of the mathematics of the "reparameterization trick" is given in goker's answer, but some motivation could be helpful. (I don't have permissions to comment on that answer; thus he
How does the reparameterization trick for VAEs work and why is it important? A reasonable example of the mathematics of the "reparameterization trick" is given in goker's answer, but some motivation could be helpful. (I don't have permissions to comment on that answer; thus here is a separate answer.) In short, we want...
How does the reparameterization trick for VAEs work and why is it important? A reasonable example of the mathematics of the "reparameterization trick" is given in goker's answer, but some motivation could be helpful. (I don't have permissions to comment on that answer; thus he
1,516
How does the reparameterization trick for VAEs work and why is it important?
Let me explain first, why do we need Reparameterization trick in VAE. VAE has encoder and decoder. Decoder randomly samples from true posterior Z~ q(zβˆ£Ο•,x). To implement encoder and decoder as a neural network, you need to backpropogate through random sampling and that is the problem because backpropogation cannot flow...
How does the reparameterization trick for VAEs work and why is it important?
Let me explain first, why do we need Reparameterization trick in VAE. VAE has encoder and decoder. Decoder randomly samples from true posterior Z~ q(zβˆ£Ο•,x). To implement encoder and decoder as a neura
How does the reparameterization trick for VAEs work and why is it important? Let me explain first, why do we need Reparameterization trick in VAE. VAE has encoder and decoder. Decoder randomly samples from true posterior Z~ q(zβˆ£Ο•,x). To implement encoder and decoder as a neural network, you need to backpropogate throug...
How does the reparameterization trick for VAEs work and why is it important? Let me explain first, why do we need Reparameterization trick in VAE. VAE has encoder and decoder. Decoder randomly samples from true posterior Z~ q(zβˆ£Ο•,x). To implement encoder and decoder as a neura
1,517
How does the reparameterization trick for VAEs work and why is it important?
I thought the explanation found in Stanford CS228 course on probabilistic graphical models was very good. It can be found here: https://ermongroup.github.io/cs228-notes/extras/vae/ I've summarized/copied the important parts here for convenience/my own understanding (although I strongly recommend just checking out the o...
How does the reparameterization trick for VAEs work and why is it important?
I thought the explanation found in Stanford CS228 course on probabilistic graphical models was very good. It can be found here: https://ermongroup.github.io/cs228-notes/extras/vae/ I've summarized/cop
How does the reparameterization trick for VAEs work and why is it important? I thought the explanation found in Stanford CS228 course on probabilistic graphical models was very good. It can be found here: https://ermongroup.github.io/cs228-notes/extras/vae/ I've summarized/copied the important parts here for convenienc...
How does the reparameterization trick for VAEs work and why is it important? I thought the explanation found in Stanford CS228 course on probabilistic graphical models was very good. It can be found here: https://ermongroup.github.io/cs228-notes/extras/vae/ I've summarized/cop
1,518
How does the reparameterization trick for VAEs work and why is it important?
We have our probablistic model. And want to recover parameters of the model. We reduce our task to optimizing variational lower bound (VLB). To do this we should be able make two things: calculate VLB get gradient of VLB Authors suggest using Monte Carlo Estimator for both. And actually they introduce this trick to ...
How does the reparameterization trick for VAEs work and why is it important?
We have our probablistic model. And want to recover parameters of the model. We reduce our task to optimizing variational lower bound (VLB). To do this we should be able make two things: calculate V
How does the reparameterization trick for VAEs work and why is it important? We have our probablistic model. And want to recover parameters of the model. We reduce our task to optimizing variational lower bound (VLB). To do this we should be able make two things: calculate VLB get gradient of VLB Authors suggest usi...
How does the reparameterization trick for VAEs work and why is it important? We have our probablistic model. And want to recover parameters of the model. We reduce our task to optimizing variational lower bound (VLB). To do this we should be able make two things: calculate V
1,519
How does the reparameterization trick for VAEs work and why is it important?
The reparameterization trick reduces the variance of the MC estimator for the gradient dramatically. So it's a variance reduction technique: Our goal is to find an estimate of $$ \nabla_\phi \mathbb E_{q(z^{(i)} \mid x^{(i)}; \phi)} \left[ \log p\left( x^{(i)} \mid z^{(i)}, w \right) \right] $$ We could use the "Score ...
How does the reparameterization trick for VAEs work and why is it important?
The reparameterization trick reduces the variance of the MC estimator for the gradient dramatically. So it's a variance reduction technique: Our goal is to find an estimate of $$ \nabla_\phi \mathbb E
How does the reparameterization trick for VAEs work and why is it important? The reparameterization trick reduces the variance of the MC estimator for the gradient dramatically. So it's a variance reduction technique: Our goal is to find an estimate of $$ \nabla_\phi \mathbb E_{q(z^{(i)} \mid x^{(i)}; \phi)} \left[ \lo...
How does the reparameterization trick for VAEs work and why is it important? The reparameterization trick reduces the variance of the MC estimator for the gradient dramatically. So it's a variance reduction technique: Our goal is to find an estimate of $$ \nabla_\phi \mathbb E
1,520
How does the reparameterization trick for VAEs work and why is it important?
The issue is not that we cannot backprop through a β€œrandom node” in any technical sense. Rather, backproping would not compute an estimate of the derivative. Without the reparameterization trick, we have no guarantee that sampling large numbers of z will help converge to the right estimate of βˆ‡ΞΈ Furthermore, this is th...
How does the reparameterization trick for VAEs work and why is it important?
The issue is not that we cannot backprop through a β€œrandom node” in any technical sense. Rather, backproping would not compute an estimate of the derivative. Without the reparameterization trick, we h
How does the reparameterization trick for VAEs work and why is it important? The issue is not that we cannot backprop through a β€œrandom node” in any technical sense. Rather, backproping would not compute an estimate of the derivative. Without the reparameterization trick, we have no guarantee that sampling large number...
How does the reparameterization trick for VAEs work and why is it important? The issue is not that we cannot backprop through a β€œrandom node” in any technical sense. Rather, backproping would not compute an estimate of the derivative. Without the reparameterization trick, we h
1,521
What misused statistical terms are worth correcting?
It can be futile to fight against shifts in language. But parameter does not mean variable In classical statistics, which in this case starts precisely with R.A. Fisher who first used the term with this meaning, a parameter is an unknown constant to be estimated, say a population mean or correlation. In mathematics, th...
What misused statistical terms are worth correcting?
It can be futile to fight against shifts in language. But parameter does not mean variable In classical statistics, which in this case starts precisely with R.A. Fisher who first used the term with th
What misused statistical terms are worth correcting? It can be futile to fight against shifts in language. But parameter does not mean variable In classical statistics, which in this case starts precisely with R.A. Fisher who first used the term with this meaning, a parameter is an unknown constant to be estimated, say...
What misused statistical terms are worth correcting? It can be futile to fight against shifts in language. But parameter does not mean variable In classical statistics, which in this case starts precisely with R.A. Fisher who first used the term with th
1,522
What misused statistical terms are worth correcting?
Some of the things I encounter: Treating significance level and CI coverage probabilities as interchangeable, so that people end up doing things like speaking of "95% significance". [What's worse is when people who make such errors point to their lecture notes -- or even textbook -- as support for this; in other word...
What misused statistical terms are worth correcting?
Some of the things I encounter: Treating significance level and CI coverage probabilities as interchangeable, so that people end up doing things like speaking of "95% significance". [What's worse is
What misused statistical terms are worth correcting? Some of the things I encounter: Treating significance level and CI coverage probabilities as interchangeable, so that people end up doing things like speaking of "95% significance". [What's worse is when people who make such errors point to their lecture notes -- o...
What misused statistical terms are worth correcting? Some of the things I encounter: Treating significance level and CI coverage probabilities as interchangeable, so that people end up doing things like speaking of "95% significance". [What's worse is
1,523
What misused statistical terms are worth correcting?
"Data" is plural. (The singular is "datum").
What misused statistical terms are worth correcting?
"Data" is plural. (The singular is "datum").
What misused statistical terms are worth correcting? "Data" is plural. (The singular is "datum").
What misused statistical terms are worth correcting? "Data" is plural. (The singular is "datum").
1,524
What misused statistical terms are worth correcting?
While not strictly a statistical term, I vote to retire endogeneity. It's used to refer to everything from reverse causation through confounding to selection and collider bias, when all people really want to do is say: "That effect is not identified".
What misused statistical terms are worth correcting?
While not strictly a statistical term, I vote to retire endogeneity. It's used to refer to everything from reverse causation through confounding to selection and collider bias, when all people really
What misused statistical terms are worth correcting? While not strictly a statistical term, I vote to retire endogeneity. It's used to refer to everything from reverse causation through confounding to selection and collider bias, when all people really want to do is say: "That effect is not identified".
What misused statistical terms are worth correcting? While not strictly a statistical term, I vote to retire endogeneity. It's used to refer to everything from reverse causation through confounding to selection and collider bias, when all people really
1,525
What misused statistical terms are worth correcting?
Percent vs. Percentage Points: If something increases from 1% to 2%, it increased by 100%. Or: you can say that it increased by 1 percentage point. Stating that the increase was 1% is very misleading.
What misused statistical terms are worth correcting?
Percent vs. Percentage Points: If something increases from 1% to 2%, it increased by 100%. Or: you can say that it increased by 1 percentage point. Stating that the increase was 1% is very mislead
What misused statistical terms are worth correcting? Percent vs. Percentage Points: If something increases from 1% to 2%, it increased by 100%. Or: you can say that it increased by 1 percentage point. Stating that the increase was 1% is very misleading.
What misused statistical terms are worth correcting? Percent vs. Percentage Points: If something increases from 1% to 2%, it increased by 100%. Or: you can say that it increased by 1 percentage point. Stating that the increase was 1% is very mislead
1,526
What misused statistical terms are worth correcting?
"Regression towards the mean" does not mean that if we've observed a certain number of iid samples below expected value, the next iid samples are likely to be above the expected value.
What misused statistical terms are worth correcting?
"Regression towards the mean" does not mean that if we've observed a certain number of iid samples below expected value, the next iid samples are likely to be above the expected value.
What misused statistical terms are worth correcting? "Regression towards the mean" does not mean that if we've observed a certain number of iid samples below expected value, the next iid samples are likely to be above the expected value.
What misused statistical terms are worth correcting? "Regression towards the mean" does not mean that if we've observed a certain number of iid samples below expected value, the next iid samples are likely to be above the expected value.
1,527
What misused statistical terms are worth correcting?
Kurtosis does not measure "peakedness." By definition, it is the expected value (average) of $Z^4$.* Thus, $|Z|$-values less than 1 (corresponding to data values within one standard deviation of the mean, where any "peak" would be) contribute very little to kurtosis; nearly all the contribution to kurtosis is from $|Z...
What misused statistical terms are worth correcting?
Kurtosis does not measure "peakedness." By definition, it is the expected value (average) of $Z^4$.* Thus, $|Z|$-values less than 1 (corresponding to data values within one standard deviation of the
What misused statistical terms are worth correcting? Kurtosis does not measure "peakedness." By definition, it is the expected value (average) of $Z^4$.* Thus, $|Z|$-values less than 1 (corresponding to data values within one standard deviation of the mean, where any "peak" would be) contribute very little to kurtosis...
What misused statistical terms are worth correcting? Kurtosis does not measure "peakedness." By definition, it is the expected value (average) of $Z^4$.* Thus, $|Z|$-values less than 1 (corresponding to data values within one standard deviation of the
1,528
What misused statistical terms are worth correcting?
I find abbreviations that aren't clearly indicated are a real problem. For example, I see things like GLM and nowhere is it specified if this means general linear model or generalized linear model. Once can usually figure out what is being referenced after digging into the context, but I find this is particularly tro...
What misused statistical terms are worth correcting?
I find abbreviations that aren't clearly indicated are a real problem. For example, I see things like GLM and nowhere is it specified if this means general linear model or generalized linear model.
What misused statistical terms are worth correcting? I find abbreviations that aren't clearly indicated are a real problem. For example, I see things like GLM and nowhere is it specified if this means general linear model or generalized linear model. Once can usually figure out what is being referenced after digging ...
What misused statistical terms are worth correcting? I find abbreviations that aren't clearly indicated are a real problem. For example, I see things like GLM and nowhere is it specified if this means general linear model or generalized linear model.
1,529
What misused statistical terms are worth correcting?
One that is common in everyday language: average To the average person out there (bitter irony fully intended), the mean, median, mode and expected value of anything seem to be the same. They have a natural tendency to do a point estimation, with the unconscious and unassailable assumption that there is an underlying...
What misused statistical terms are worth correcting?
One that is common in everyday language: average To the average person out there (bitter irony fully intended), the mean, median, mode and expected value of anything seem to be the same. They have a
What misused statistical terms are worth correcting? One that is common in everyday language: average To the average person out there (bitter irony fully intended), the mean, median, mode and expected value of anything seem to be the same. They have a natural tendency to do a point estimation, with the unconscious an...
What misused statistical terms are worth correcting? One that is common in everyday language: average To the average person out there (bitter irony fully intended), the mean, median, mode and expected value of anything seem to be the same. They have a
1,530
What misused statistical terms are worth correcting?
Linear means: Line-like. As in $y = a + bx$ from elementary algebra. In this respect nonlinear means things like $y = a + bx + cx^{2}$, and also things like $y = ax^{b}$ Linear in the parameters being estimated. As in a regression model (linear, logistic, GLM, etc.) entails a sum of products of scalar parameters and i...
What misused statistical terms are worth correcting?
Linear means: Line-like. As in $y = a + bx$ from elementary algebra. In this respect nonlinear means things like $y = a + bx + cx^{2}$, and also things like $y = ax^{b}$ Linear in the parameters bein
What misused statistical terms are worth correcting? Linear means: Line-like. As in $y = a + bx$ from elementary algebra. In this respect nonlinear means things like $y = a + bx + cx^{2}$, and also things like $y = ax^{b}$ Linear in the parameters being estimated. As in a regression model (linear, logistic, GLM, etc.)...
What misused statistical terms are worth correcting? Linear means: Line-like. As in $y = a + bx$ from elementary algebra. In this respect nonlinear means things like $y = a + bx + cx^{2}$, and also things like $y = ax^{b}$ Linear in the parameters bein
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What misused statistical terms are worth correcting?
The question was about uses of statistical terms that we should CARE to correct. I have been correcting my millennial kids' use of the term 'random' to mean things that are the opposite of random for 10 years now. Considering how many of my trainees struggle to produce a random data sample that is actually random, whic...
What misused statistical terms are worth correcting?
The question was about uses of statistical terms that we should CARE to correct. I have been correcting my millennial kids' use of the term 'random' to mean things that are the opposite of random for
What misused statistical terms are worth correcting? The question was about uses of statistical terms that we should CARE to correct. I have been correcting my millennial kids' use of the term 'random' to mean things that are the opposite of random for 10 years now. Considering how many of my trainees struggle to produ...
What misused statistical terms are worth correcting? The question was about uses of statistical terms that we should CARE to correct. I have been correcting my millennial kids' use of the term 'random' to mean things that are the opposite of random for
1,532
What misused statistical terms are worth correcting?
There are already too many great examples mentioned by Glen and Nick... not much left! Some aspects of regression error term and residual (it is somewhat funny when people are proud their residuals are uncorrelated with the regressors) prediction and estimation (should we even stop making the distinction when they are...
What misused statistical terms are worth correcting?
There are already too many great examples mentioned by Glen and Nick... not much left! Some aspects of regression error term and residual (it is somewhat funny when people are proud their residuals a
What misused statistical terms are worth correcting? There are already too many great examples mentioned by Glen and Nick... not much left! Some aspects of regression error term and residual (it is somewhat funny when people are proud their residuals are uncorrelated with the regressors) prediction and estimation (sho...
What misused statistical terms are worth correcting? There are already too many great examples mentioned by Glen and Nick... not much left! Some aspects of regression error term and residual (it is somewhat funny when people are proud their residuals a
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What misused statistical terms are worth correcting?
In insurance environments especially, it is common to use variance to refer to any sort of difference, rather than the mean of the squared differences between each data point and the mean of the data set.
What misused statistical terms are worth correcting?
In insurance environments especially, it is common to use variance to refer to any sort of difference, rather than the mean of the squared differences between each data point and the mean of the data
What misused statistical terms are worth correcting? In insurance environments especially, it is common to use variance to refer to any sort of difference, rather than the mean of the squared differences between each data point and the mean of the data set.
What misused statistical terms are worth correcting? In insurance environments especially, it is common to use variance to refer to any sort of difference, rather than the mean of the squared differences between each data point and the mean of the data
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What misused statistical terms are worth correcting?
Fixed effects and random effects can mean different things for different people. In econometrics fixed effects are actually random and when you think about it every effect in statistics is random so naming something random does not give any meaningful additional information.
What misused statistical terms are worth correcting?
Fixed effects and random effects can mean different things for different people. In econometrics fixed effects are actually random and when you think about it every effect in statistics is random so n
What misused statistical terms are worth correcting? Fixed effects and random effects can mean different things for different people. In econometrics fixed effects are actually random and when you think about it every effect in statistics is random so naming something random does not give any meaningful additional info...
What misused statistical terms are worth correcting? Fixed effects and random effects can mean different things for different people. In econometrics fixed effects are actually random and when you think about it every effect in statistics is random so n
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What misused statistical terms are worth correcting?
Bayesian Students learning it might not have trouble telling you whether something "looks" Bayesian, but ask them to solve a problem with a frequentist and a Bayesian approach and they'll probably fail. In my experience students end up being taught that it's just a philosophical difference, with no concrete example tha...
What misused statistical terms are worth correcting?
Bayesian Students learning it might not have trouble telling you whether something "looks" Bayesian, but ask them to solve a problem with a frequentist and a Bayesian approach and they'll probably fai
What misused statistical terms are worth correcting? Bayesian Students learning it might not have trouble telling you whether something "looks" Bayesian, but ask them to solve a problem with a frequentist and a Bayesian approach and they'll probably fail. In my experience students end up being taught that it's just a p...
What misused statistical terms are worth correcting? Bayesian Students learning it might not have trouble telling you whether something "looks" Bayesian, but ask them to solve a problem with a frequentist and a Bayesian approach and they'll probably fai
1,536
What misused statistical terms are worth correcting?
Risk Risk does not mean probability Risk is the sum of the costs of all outcomes, each of these costs multiplied by the probability of them happening. Risk is usually weighed against reward which is the gain that we are seeking to achieve. Here is one example: How Deadly Is Your Kilowatt. Here the risks β€” number of de...
What misused statistical terms are worth correcting?
Risk Risk does not mean probability Risk is the sum of the costs of all outcomes, each of these costs multiplied by the probability of them happening. Risk is usually weighed against reward which is
What misused statistical terms are worth correcting? Risk Risk does not mean probability Risk is the sum of the costs of all outcomes, each of these costs multiplied by the probability of them happening. Risk is usually weighed against reward which is the gain that we are seeking to achieve. Here is one example: How D...
What misused statistical terms are worth correcting? Risk Risk does not mean probability Risk is the sum of the costs of all outcomes, each of these costs multiplied by the probability of them happening. Risk is usually weighed against reward which is
1,537
What is rank deficiency, and how to deal with it?
Rank deficiency in this context says there is insufficient information contained in your data to estimate the model you desire. It stems from many origins. I'll talk here about modeling in a fairly general context, rather than explicitly logistic regression, but everything still applies to the specific context. The def...
What is rank deficiency, and how to deal with it?
Rank deficiency in this context says there is insufficient information contained in your data to estimate the model you desire. It stems from many origins. I'll talk here about modeling in a fairly ge
What is rank deficiency, and how to deal with it? Rank deficiency in this context says there is insufficient information contained in your data to estimate the model you desire. It stems from many origins. I'll talk here about modeling in a fairly general context, rather than explicitly logistic regression, but everyth...
What is rank deficiency, and how to deal with it? Rank deficiency in this context says there is insufficient information contained in your data to estimate the model you desire. It stems from many origins. I'll talk here about modeling in a fairly ge
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What is rank deficiency, and how to deal with it?
For the definition of the rank of a matrix, you can refer to any good textbook on linear algebra, or have a look at the Wikipedia page. A $n \times p$ matrix $X$ is said to be full rank if $n \geq p$, and its columns are not a linear combination of each other. In that case, the $p \times p$ matrix $X^TX$ is positive de...
What is rank deficiency, and how to deal with it?
For the definition of the rank of a matrix, you can refer to any good textbook on linear algebra, or have a look at the Wikipedia page. A $n \times p$ matrix $X$ is said to be full rank if $n \geq p$,
What is rank deficiency, and how to deal with it? For the definition of the rank of a matrix, you can refer to any good textbook on linear algebra, or have a look at the Wikipedia page. A $n \times p$ matrix $X$ is said to be full rank if $n \geq p$, and its columns are not a linear combination of each other. In that c...
What is rank deficiency, and how to deal with it? For the definition of the rank of a matrix, you can refer to any good textbook on linear algebra, or have a look at the Wikipedia page. A $n \times p$ matrix $X$ is said to be full rank if $n \geq p$,
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What is rank deficiency, and how to deal with it?
user974's answer is fantastic from a modelling perspective and gui11aume's answer is fantastic from a mathematical perspective. I want to refine the former answer strictly from a mixed modelling perspective: specifically a generalized mixed modelling (GLMM) perspective. As you can see, you have referenced the R functio...
What is rank deficiency, and how to deal with it?
user974's answer is fantastic from a modelling perspective and gui11aume's answer is fantastic from a mathematical perspective. I want to refine the former answer strictly from a mixed modelling persp
What is rank deficiency, and how to deal with it? user974's answer is fantastic from a modelling perspective and gui11aume's answer is fantastic from a mathematical perspective. I want to refine the former answer strictly from a mixed modelling perspective: specifically a generalized mixed modelling (GLMM) perspective....
What is rank deficiency, and how to deal with it? user974's answer is fantastic from a modelling perspective and gui11aume's answer is fantastic from a mathematical perspective. I want to refine the former answer strictly from a mixed modelling persp
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What is rank deficiency, and how to deal with it?
I also kept getting warnings about rank deficiency. In my case it seemed to be caused by the fact that I had a categorical variable where some of the categories were empty/not represented in the training set. When I created a category called other for the different low-frequency categories, I got rid of the warning. Th...
What is rank deficiency, and how to deal with it?
I also kept getting warnings about rank deficiency. In my case it seemed to be caused by the fact that I had a categorical variable where some of the categories were empty/not represented in the train
What is rank deficiency, and how to deal with it? I also kept getting warnings about rank deficiency. In my case it seemed to be caused by the fact that I had a categorical variable where some of the categories were empty/not represented in the training set. When I created a category called other for the different low-...
What is rank deficiency, and how to deal with it? I also kept getting warnings about rank deficiency. In my case it seemed to be caused by the fact that I had a categorical variable where some of the categories were empty/not represented in the train
1,541
Including the interaction but not the main effects in a model
In my experience, not only is it necessary to have all lower order effects in the model when they are connected to higher order effects, but it is also important to properly model (e.g., allowing to be nonlinear) main effects that are seemingly unrelated to the factors in the interactions of interest. That's because i...
Including the interaction but not the main effects in a model
In my experience, not only is it necessary to have all lower order effects in the model when they are connected to higher order effects, but it is also important to properly model (e.g., allowing to b
Including the interaction but not the main effects in a model In my experience, not only is it necessary to have all lower order effects in the model when they are connected to higher order effects, but it is also important to properly model (e.g., allowing to be nonlinear) main effects that are seemingly unrelated to ...
Including the interaction but not the main effects in a model In my experience, not only is it necessary to have all lower order effects in the model when they are connected to higher order effects, but it is also important to properly model (e.g., allowing to b
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Including the interaction but not the main effects in a model
You ask whether it's ever valid. Let me provide a common example, whose elucidation may suggest additional analytical approaches for you. The simplest example of an interaction is a model with one dependent variable $Z$ and two independent variables $X$, $Y$ in the form $$Z = \alpha + \beta' X + \gamma' Y + \delta' X ...
Including the interaction but not the main effects in a model
You ask whether it's ever valid. Let me provide a common example, whose elucidation may suggest additional analytical approaches for you. The simplest example of an interaction is a model with one de
Including the interaction but not the main effects in a model You ask whether it's ever valid. Let me provide a common example, whose elucidation may suggest additional analytical approaches for you. The simplest example of an interaction is a model with one dependent variable $Z$ and two independent variables $X$, $Y...
Including the interaction but not the main effects in a model You ask whether it's ever valid. Let me provide a common example, whose elucidation may suggest additional analytical approaches for you. The simplest example of an interaction is a model with one de
1,543
Including the interaction but not the main effects in a model
While it is often stated in textbooks that one should never include an interaction in a model without the corresponding main effects, there are certainly examples where this would make perfect sense. I'll give you the simplest example I can imagine. Suppose subjects randomly assigned to two groups are measured twice, ...
Including the interaction but not the main effects in a model
While it is often stated in textbooks that one should never include an interaction in a model without the corresponding main effects, there are certainly examples where this would make perfect sense.
Including the interaction but not the main effects in a model While it is often stated in textbooks that one should never include an interaction in a model without the corresponding main effects, there are certainly examples where this would make perfect sense. I'll give you the simplest example I can imagine. Suppose...
Including the interaction but not the main effects in a model While it is often stated in textbooks that one should never include an interaction in a model without the corresponding main effects, there are certainly examples where this would make perfect sense.
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Including the interaction but not the main effects in a model
The reason to keep the main effects in the model is for identifiability. Hence, if the purpose is statistical inference about each of the effects, you should keep the main effects in the model. However, if your modeling purpose is solely to predict new values, then it is perfectly legitimate to include only the interac...
Including the interaction but not the main effects in a model
The reason to keep the main effects in the model is for identifiability. Hence, if the purpose is statistical inference about each of the effects, you should keep the main effects in the model. Howeve
Including the interaction but not the main effects in a model The reason to keep the main effects in the model is for identifiability. Hence, if the purpose is statistical inference about each of the effects, you should keep the main effects in the model. However, if your modeling purpose is solely to predict new value...
Including the interaction but not the main effects in a model The reason to keep the main effects in the model is for identifiability. Hence, if the purpose is statistical inference about each of the effects, you should keep the main effects in the model. Howeve
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Including the interaction but not the main effects in a model
this is implicit in many of answers others have given but the simple point is that models w/ a product term but w/ & w/o the moderator & predictor are just different models. Figure out what each means given the process you are modeling and whether a model w/o the moderator & predictor makes more sense given your theory...
Including the interaction but not the main effects in a model
this is implicit in many of answers others have given but the simple point is that models w/ a product term but w/ & w/o the moderator & predictor are just different models. Figure out what each means
Including the interaction but not the main effects in a model this is implicit in many of answers others have given but the simple point is that models w/ a product term but w/ & w/o the moderator & predictor are just different models. Figure out what each means given the process you are modeling and whether a model w/...
Including the interaction but not the main effects in a model this is implicit in many of answers others have given but the simple point is that models w/ a product term but w/ & w/o the moderator & predictor are just different models. Figure out what each means
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Including the interaction but not the main effects in a model
Arguably, it depends on what you're using your model for. But I've never seen a reason not to run and describe models with main effects, even in cases where the hypothesis is only about the interaction.
Including the interaction but not the main effects in a model
Arguably, it depends on what you're using your model for. But I've never seen a reason not to run and describe models with main effects, even in cases where the hypothesis is only about the interacti
Including the interaction but not the main effects in a model Arguably, it depends on what you're using your model for. But I've never seen a reason not to run and describe models with main effects, even in cases where the hypothesis is only about the interaction.
Including the interaction but not the main effects in a model Arguably, it depends on what you're using your model for. But I've never seen a reason not to run and describe models with main effects, even in cases where the hypothesis is only about the interacti
1,547
Including the interaction but not the main effects in a model
Various texts on regression will tell you that you should never include an interaction term without the base effects --- that is not correct. One circumstance where it is appropriate to include an interaction term in your model without a base effect is when you have nested variables in your model. For example, if you...
Including the interaction but not the main effects in a model
Various texts on regression will tell you that you should never include an interaction term without the base effects --- that is not correct. One circumstance where it is appropriate to include an in
Including the interaction but not the main effects in a model Various texts on regression will tell you that you should never include an interaction term without the base effects --- that is not correct. One circumstance where it is appropriate to include an interaction term in your model without a base effect is when...
Including the interaction but not the main effects in a model Various texts on regression will tell you that you should never include an interaction term without the base effects --- that is not correct. One circumstance where it is appropriate to include an in
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Including the interaction but not the main effects in a model
Both x and y will be correlated with xy (unless you have taken a specific measure to prevent this by using centering). Thus if you obtain a substantial interaction effect with your approach, it will likely amount to one or more main effects masquerading as an interaction. This is not going to produce clear, interpret...
Including the interaction but not the main effects in a model
Both x and y will be correlated with xy (unless you have taken a specific measure to prevent this by using centering). Thus if you obtain a substantial interaction effect with your approach, it will
Including the interaction but not the main effects in a model Both x and y will be correlated with xy (unless you have taken a specific measure to prevent this by using centering). Thus if you obtain a substantial interaction effect with your approach, it will likely amount to one or more main effects masquerading as ...
Including the interaction but not the main effects in a model Both x and y will be correlated with xy (unless you have taken a specific measure to prevent this by using centering). Thus if you obtain a substantial interaction effect with your approach, it will
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Including the interaction but not the main effects in a model
I would suggest it is simply a special case of model uncertainty. From a Bayesian perspective, you simply treat this in exactly the same way you would treat any other kind of uncertainty, by either: Calculating its probability, if it is the object of interest Integrating or averaging it out, if it is not of interest,...
Including the interaction but not the main effects in a model
I would suggest it is simply a special case of model uncertainty. From a Bayesian perspective, you simply treat this in exactly the same way you would treat any other kind of uncertainty, by either:
Including the interaction but not the main effects in a model I would suggest it is simply a special case of model uncertainty. From a Bayesian perspective, you simply treat this in exactly the same way you would treat any other kind of uncertainty, by either: Calculating its probability, if it is the object of inter...
Including the interaction but not the main effects in a model I would suggest it is simply a special case of model uncertainty. From a Bayesian perspective, you simply treat this in exactly the same way you would treat any other kind of uncertainty, by either:
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Including the interaction but not the main effects in a model
I will borrow a paragraph from the book An introduction to survival analysis using Stata by M.Cleves, R.Gutierrez, W.Gould, Y.Marchenko edited by Stata press to answer to your question. It is common to read that interaction effects should be included in the model only when the corresponding main effects are also inclu...
Including the interaction but not the main effects in a model
I will borrow a paragraph from the book An introduction to survival analysis using Stata by M.Cleves, R.Gutierrez, W.Gould, Y.Marchenko edited by Stata press to answer to your question. It is common
Including the interaction but not the main effects in a model I will borrow a paragraph from the book An introduction to survival analysis using Stata by M.Cleves, R.Gutierrez, W.Gould, Y.Marchenko edited by Stata press to answer to your question. It is common to read that interaction effects should be included in the...
Including the interaction but not the main effects in a model I will borrow a paragraph from the book An introduction to survival analysis using Stata by M.Cleves, R.Gutierrez, W.Gould, Y.Marchenko edited by Stata press to answer to your question. It is common
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Including the interaction but not the main effects in a model
There are various processes in nature that involve only an interaction effect and laws that decribe them. For instance Ohm's law. In psychology you have for instance the performance model of Vroom (1964): Performance = Ability x Motivation.Now, you might expect finding an significant interaction effect when this law is...
Including the interaction but not the main effects in a model
There are various processes in nature that involve only an interaction effect and laws that decribe them. For instance Ohm's law. In psychology you have for instance the performance model of Vroom (19
Including the interaction but not the main effects in a model There are various processes in nature that involve only an interaction effect and laws that decribe them. For instance Ohm's law. In psychology you have for instance the performance model of Vroom (1964): Performance = Ability x Motivation.Now, you might exp...
Including the interaction but not the main effects in a model There are various processes in nature that involve only an interaction effect and laws that decribe them. For instance Ohm's law. In psychology you have for instance the performance model of Vroom (19
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Including the interaction but not the main effects in a model
F = m*a, force equals mass times acceleration. It is not represented as F = m + a + ma, or some other linear combination of those parameters. Indeed, only the interaction between mass and acceleration would make sense physically.
Including the interaction but not the main effects in a model
F = m*a, force equals mass times acceleration. It is not represented as F = m + a + ma, or some other linear combination of those parameters. Indeed, only the interaction between mass and acceleration
Including the interaction but not the main effects in a model F = m*a, force equals mass times acceleration. It is not represented as F = m + a + ma, or some other linear combination of those parameters. Indeed, only the interaction between mass and acceleration would make sense physically.
Including the interaction but not the main effects in a model F = m*a, force equals mass times acceleration. It is not represented as F = m + a + ma, or some other linear combination of those parameters. Indeed, only the interaction between mass and acceleration
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Including the interaction but not the main effects in a model
Is it ever valid to include a two-way interaction without main effect? Yes it can be valid and even necessary. If for example in 2. you would include a factor for main effect (average difference of blue vs red condition) this would make the model worse. What if your hypothesis is only about the interaction, do you st...
Including the interaction but not the main effects in a model
Is it ever valid to include a two-way interaction without main effect? Yes it can be valid and even necessary. If for example in 2. you would include a factor for main effect (average difference of b
Including the interaction but not the main effects in a model Is it ever valid to include a two-way interaction without main effect? Yes it can be valid and even necessary. If for example in 2. you would include a factor for main effect (average difference of blue vs red condition) this would make the model worse. Wh...
Including the interaction but not the main effects in a model Is it ever valid to include a two-way interaction without main effect? Yes it can be valid and even necessary. If for example in 2. you would include a factor for main effect (average difference of b
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Including the interaction but not the main effects in a model
It is very rarely a good idea to include an interaction term without the main effects involved in it. David Rindskopf of CCNY has written some papers about those rare instances. EDIT One such paper is https://psycnet.apa.org/record/1990-27319-001 Nonstandard loglinear models published in Psychological Bulletin vol 108 ...
Including the interaction but not the main effects in a model
It is very rarely a good idea to include an interaction term without the main effects involved in it. David Rindskopf of CCNY has written some papers about those rare instances. EDIT One such paper is
Including the interaction but not the main effects in a model It is very rarely a good idea to include an interaction term without the main effects involved in it. David Rindskopf of CCNY has written some papers about those rare instances. EDIT One such paper is https://psycnet.apa.org/record/1990-27319-001 Nonstandard...
Including the interaction but not the main effects in a model It is very rarely a good idea to include an interaction term without the main effects involved in it. David Rindskopf of CCNY has written some papers about those rare instances. EDIT One such paper is
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Including the interaction but not the main effects in a model
This one is tricky and happened to me in my last project. I would explain it this way: lets say you had variables A and B which came out significant independently and by a business sense you thought that an interaction of A and B seems good. You included the interaction which came out to be significant but B lost its s...
Including the interaction but not the main effects in a model
This one is tricky and happened to me in my last project. I would explain it this way: lets say you had variables A and B which came out significant independently and by a business sense you thought t
Including the interaction but not the main effects in a model This one is tricky and happened to me in my last project. I would explain it this way: lets say you had variables A and B which came out significant independently and by a business sense you thought that an interaction of A and B seems good. You included the...
Including the interaction but not the main effects in a model This one is tricky and happened to me in my last project. I would explain it this way: lets say you had variables A and B which came out significant independently and by a business sense you thought t
1,556
Including the interaction but not the main effects in a model
If the variables in question are categorical, then including interactions without the main effects is just a reparameterizations of the model, and the choice of parameterization depends on what you are trying to accomplish with your model. Interacting continuous variables with other continuous variables ore with catego...
Including the interaction but not the main effects in a model
If the variables in question are categorical, then including interactions without the main effects is just a reparameterizations of the model, and the choice of parameterization depends on what you ar
Including the interaction but not the main effects in a model If the variables in question are categorical, then including interactions without the main effects is just a reparameterizations of the model, and the choice of parameterization depends on what you are trying to accomplish with your model. Interacting contin...
Including the interaction but not the main effects in a model If the variables in question are categorical, then including interactions without the main effects is just a reparameterizations of the model, and the choice of parameterization depends on what you ar
1,557
Including the interaction but not the main effects in a model
Yes this can be valid, although it is rare. But in this case you still need to model the main effects, which you will afterward regress out. Indeed, in some models, only the interaction is interesting, such as drug testing/clinical models. This is for example the basis of the Generalized PsychoPhysiological Interaction...
Including the interaction but not the main effects in a model
Yes this can be valid, although it is rare. But in this case you still need to model the main effects, which you will afterward regress out. Indeed, in some models, only the interaction is interesting
Including the interaction but not the main effects in a model Yes this can be valid, although it is rare. But in this case you still need to model the main effects, which you will afterward regress out. Indeed, in some models, only the interaction is interesting, such as drug testing/clinical models. This is for exampl...
Including the interaction but not the main effects in a model Yes this can be valid, although it is rare. But in this case you still need to model the main effects, which you will afterward regress out. Indeed, in some models, only the interaction is interesting
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Including the interaction but not the main effects in a model
The short answer: If you include interaction in the fixed effects, then the main effects are automatically included whether or not you specifically include them in your code. The only difference is your parametrization, i.e., what the parameters in your model mean (e.g., are they group means or are they differences fro...
Including the interaction but not the main effects in a model
The short answer: If you include interaction in the fixed effects, then the main effects are automatically included whether or not you specifically include them in your code. The only difference is yo
Including the interaction but not the main effects in a model The short answer: If you include interaction in the fixed effects, then the main effects are automatically included whether or not you specifically include them in your code. The only difference is your parametrization, i.e., what the parameters in your mode...
Including the interaction but not the main effects in a model The short answer: If you include interaction in the fixed effects, then the main effects are automatically included whether or not you specifically include them in your code. The only difference is yo
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T-test for non normal when N>50?
Normality assumption of a t-test Consider a large population from which you could take many different samples of a particular size. (In a particular study, you generally collect just one of these samples.) The t-test assumes that the means of the different samples are normally distributed; it does not assume that the p...
T-test for non normal when N>50?
Normality assumption of a t-test Consider a large population from which you could take many different samples of a particular size. (In a particular study, you generally collect just one of these samp
T-test for non normal when N>50? Normality assumption of a t-test Consider a large population from which you could take many different samples of a particular size. (In a particular study, you generally collect just one of these samples.) The t-test assumes that the means of the different samples are normally distribut...
T-test for non normal when N>50? Normality assumption of a t-test Consider a large population from which you could take many different samples of a particular size. (In a particular study, you generally collect just one of these samp
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T-test for non normal when N>50?
The central limit theorem is less useful than one might think in this context. First, as someone pointed out already, one does not know if the current sample size is "large enough". Secondly, the CLT is more about achieving the desired type I error than about type II error. In other words, the t-test can be uncompet...
T-test for non normal when N>50?
The central limit theorem is less useful than one might think in this context. First, as someone pointed out already, one does not know if the current sample size is "large enough". Secondly, the CL
T-test for non normal when N>50? The central limit theorem is less useful than one might think in this context. First, as someone pointed out already, one does not know if the current sample size is "large enough". Secondly, the CLT is more about achieving the desired type I error than about type II error. In other ...
T-test for non normal when N>50? The central limit theorem is less useful than one might think in this context. First, as someone pointed out already, one does not know if the current sample size is "large enough". Secondly, the CL
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T-test for non normal when N>50?
See my previous answer to a question on the robustness of the t-test. In particular, I recommend playing around with the onlinestatsbook applet. The image below is based on the following scenario: null hypothesis is true fairly severe skewness same distribution in both groups same variance in both groups sample size p...
T-test for non normal when N>50?
See my previous answer to a question on the robustness of the t-test. In particular, I recommend playing around with the onlinestatsbook applet. The image below is based on the following scenario: nu
T-test for non normal when N>50? See my previous answer to a question on the robustness of the t-test. In particular, I recommend playing around with the onlinestatsbook applet. The image below is based on the following scenario: null hypothesis is true fairly severe skewness same distribution in both groups same vari...
T-test for non normal when N>50? See my previous answer to a question on the robustness of the t-test. In particular, I recommend playing around with the onlinestatsbook applet. The image below is based on the following scenario: nu
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T-test for non normal when N>50?
In my experience with just the one-sample t-test, I have found that the skew of the distributions is more important than the kurtosis, say. For non-skewed but fat-tailed distributions (a t with 5 degrees of freedom, a Tukey h-distribution with $h=0.24999$, etc), I have found that 40 samples has always been sufficient t...
T-test for non normal when N>50?
In my experience with just the one-sample t-test, I have found that the skew of the distributions is more important than the kurtosis, say. For non-skewed but fat-tailed distributions (a t with 5 degr
T-test for non normal when N>50? In my experience with just the one-sample t-test, I have found that the skew of the distributions is more important than the kurtosis, say. For non-skewed but fat-tailed distributions (a t with 5 degrees of freedom, a Tukey h-distribution with $h=0.24999$, etc), I have found that 40 sam...
T-test for non normal when N>50? In my experience with just the one-sample t-test, I have found that the skew of the distributions is more important than the kurtosis, say. For non-skewed but fat-tailed distributions (a t with 5 degr
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T-test for non normal when N>50?
The central limit theorem establishes (under the required conditions) that the numerator of the t-statistic is asymptotically normal. The t-statistic also has a denominator. To have a t-distribution you'd need the denominator to be independent and square-root-of-a-chi-square-on-its-df. And we know it won't be independe...
T-test for non normal when N>50?
The central limit theorem establishes (under the required conditions) that the numerator of the t-statistic is asymptotically normal. The t-statistic also has a denominator. To have a t-distribution y
T-test for non normal when N>50? The central limit theorem establishes (under the required conditions) that the numerator of the t-statistic is asymptotically normal. The t-statistic also has a denominator. To have a t-distribution you'd need the denominator to be independent and square-root-of-a-chi-square-on-its-df. ...
T-test for non normal when N>50? The central limit theorem establishes (under the required conditions) that the numerator of the t-statistic is asymptotically normal. The t-statistic also has a denominator. To have a t-distribution y
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T-test for non normal when N>50?
Yes, the Central Limit Theorem tells us this is true. So long as you avoid extremely heavy-tailed traits, non-Normality presents no problems in moderate-to-large samples. Here's a helpful review paper; http://www.annualreviews.org/doi/pdf/10.1146/annurev.publhealth.23.100901.140546 The Wilcoxon test (mentioned by other...
T-test for non normal when N>50?
Yes, the Central Limit Theorem tells us this is true. So long as you avoid extremely heavy-tailed traits, non-Normality presents no problems in moderate-to-large samples. Here's a helpful review paper
T-test for non normal when N>50? Yes, the Central Limit Theorem tells us this is true. So long as you avoid extremely heavy-tailed traits, non-Normality presents no problems in moderate-to-large samples. Here's a helpful review paper; http://www.annualreviews.org/doi/pdf/10.1146/annurev.publhealth.23.100901.140546 The ...
T-test for non normal when N>50? Yes, the Central Limit Theorem tells us this is true. So long as you avoid extremely heavy-tailed traits, non-Normality presents no problems in moderate-to-large samples. Here's a helpful review paper
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T-test for non normal when N>50?
About the use of Wilcoxon-Mann-Whitney test as an alternative I recommend the paper The Wilcoxon-Man-Whitney test under scrutiny As a test of means or medians, the Wilcoxon–Mann–Whitney (WMW) test can be severely nonrobust for deviations from the pure shift model. These are the recommendation of the authors of the pape...
T-test for non normal when N>50?
About the use of Wilcoxon-Mann-Whitney test as an alternative I recommend the paper The Wilcoxon-Man-Whitney test under scrutiny As a test of means or medians, the Wilcoxon–Mann–Whitney (WMW) test can
T-test for non normal when N>50? About the use of Wilcoxon-Mann-Whitney test as an alternative I recommend the paper The Wilcoxon-Man-Whitney test under scrutiny As a test of means or medians, the Wilcoxon–Mann–Whitney (WMW) test can be severely nonrobust for deviations from the pure shift model. These are the recommen...
T-test for non normal when N>50? About the use of Wilcoxon-Mann-Whitney test as an alternative I recommend the paper The Wilcoxon-Man-Whitney test under scrutiny As a test of means or medians, the Wilcoxon–Mann–Whitney (WMW) test can
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What is the difference between zero-inflated and hurdle models?
Thank you for the interesting question! Difference: One limitation of standard count models is that the zeros and the nonzeros (positives) are assumed to come from the same data-generating process. With hurdle models, these two processes are not constrained to be the same. The basic idea is that a Ber...
What is the difference between zero-inflated and hurdle models?
Thank you for the interesting question! Difference: One limitation of standard count models is that the zeros and the nonzeros (positives) are assumed to come from the same data-generating p
What is the difference between zero-inflated and hurdle models? Thank you for the interesting question! Difference: One limitation of standard count models is that the zeros and the nonzeros (positives) are assumed to come from the same data-generating process. With hurdle models, these two processes are not...
What is the difference between zero-inflated and hurdle models? Thank you for the interesting question! Difference: One limitation of standard count models is that the zeros and the nonzeros (positives) are assumed to come from the same data-generating p
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What is the difference between zero-inflated and hurdle models?
Hurdle models assume that there is only one process by which a zero can be produced, while zero-inflated models assume that there are 2 different processes that can produce a zero. Hurdle models assume 2 types of subjects: (1) those who never experience the outcome and (2) those who always experience the outcome at lea...
What is the difference between zero-inflated and hurdle models?
Hurdle models assume that there is only one process by which a zero can be produced, while zero-inflated models assume that there are 2 different processes that can produce a zero. Hurdle models assum
What is the difference between zero-inflated and hurdle models? Hurdle models assume that there is only one process by which a zero can be produced, while zero-inflated models assume that there are 2 different processes that can produce a zero. Hurdle models assume 2 types of subjects: (1) those who never experience th...
What is the difference between zero-inflated and hurdle models? Hurdle models assume that there is only one process by which a zero can be produced, while zero-inflated models assume that there are 2 different processes that can produce a zero. Hurdle models assum
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What is the difference between zero-inflated and hurdle models?
in ZIP model $y_i$~0 with probability $\pi$ and $y_i$~ Poisson($\lambda$) distribution with probability $1-\pi$, thus the ZIP model is mixture model with 2 components and: $$\Pr (y_j = 0) = \pi + (1 - \pi) e^{-\lambda}$$ $$\Pr (y_j = x_i) = (1 - \pi) \frac{\lambda^{x_i} e^{-\lambda}} {x_i!},\qquad x_i \ge 1$$ and in a...
What is the difference between zero-inflated and hurdle models?
in ZIP model $y_i$~0 with probability $\pi$ and $y_i$~ Poisson($\lambda$) distribution with probability $1-\pi$, thus the ZIP model is mixture model with 2 components and: $$\Pr (y_j = 0) = \pi + (1
What is the difference between zero-inflated and hurdle models? in ZIP model $y_i$~0 with probability $\pi$ and $y_i$~ Poisson($\lambda$) distribution with probability $1-\pi$, thus the ZIP model is mixture model with 2 components and: $$\Pr (y_j = 0) = \pi + (1 - \pi) e^{-\lambda}$$ $$\Pr (y_j = x_i) = (1 - \pi) \fra...
What is the difference between zero-inflated and hurdle models? in ZIP model $y_i$~0 with probability $\pi$ and $y_i$~ Poisson($\lambda$) distribution with probability $1-\pi$, thus the ZIP model is mixture model with 2 components and: $$\Pr (y_j = 0) = \pi + (1
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What is the difference between zero-inflated and hurdle models?
Regarding hurdle models, here's a quote from Advances in Mathematical and Statistical Modeling (Arnold, Balakrishnan, Sarabia, & MΓ­nguez, 2008): The hurdle model is characterized by the process below the hurdle and the one above. Obviously, the most widely used hurdle model is the one that sets the hurdle at zero. For...
What is the difference between zero-inflated and hurdle models?
Regarding hurdle models, here's a quote from Advances in Mathematical and Statistical Modeling (Arnold, Balakrishnan, Sarabia, & MΓ­nguez, 2008): The hurdle model is characterized by the process below
What is the difference between zero-inflated and hurdle models? Regarding hurdle models, here's a quote from Advances in Mathematical and Statistical Modeling (Arnold, Balakrishnan, Sarabia, & MΓ­nguez, 2008): The hurdle model is characterized by the process below the hurdle and the one above. Obviously, the most widel...
What is the difference between zero-inflated and hurdle models? Regarding hurdle models, here's a quote from Advances in Mathematical and Statistical Modeling (Arnold, Balakrishnan, Sarabia, & MΓ­nguez, 2008): The hurdle model is characterized by the process below
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When should linear regression be called "machine learning"?
Answering your question with a question: what exactly is machine learning? Trevor Hastie, Robert Tibshirani and Jerome Friedman in The Elements of Statistical Learning, Kevin P. Murphy in Machine Learning A Probabilistic Perspective, Christopher Bishop in Pattern Recognition and Machine Learning, Ian Goodfellow, Yoshu...
When should linear regression be called "machine learning"?
Answering your question with a question: what exactly is machine learning? Trevor Hastie, Robert Tibshirani and Jerome Friedman in The Elements of Statistical Learning, Kevin P. Murphy in Machine Lear
When should linear regression be called "machine learning"? Answering your question with a question: what exactly is machine learning? Trevor Hastie, Robert Tibshirani and Jerome Friedman in The Elements of Statistical Learning, Kevin P. Murphy in Machine Learning A Probabilistic Perspective, Christopher Bishop in Patt...
When should linear regression be called "machine learning"? Answering your question with a question: what exactly is machine learning? Trevor Hastie, Robert Tibshirani and Jerome Friedman in The Elements of Statistical Learning, Kevin P. Murphy in Machine Lear
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When should linear regression be called "machine learning"?
Linear regression is definitely an algorithm that can be used in machine learning. But, reductio ad absurdum: Anyone with a copy of Excel can fit a linear model. Even restricting ourselves to linear models, there are a few more things to consider when discussing machine learning: Machine learning on business problem...
When should linear regression be called "machine learning"?
Linear regression is definitely an algorithm that can be used in machine learning. But, reductio ad absurdum: Anyone with a copy of Excel can fit a linear model. Even restricting ourselves to linear
When should linear regression be called "machine learning"? Linear regression is definitely an algorithm that can be used in machine learning. But, reductio ad absurdum: Anyone with a copy of Excel can fit a linear model. Even restricting ourselves to linear models, there are a few more things to consider when discus...
When should linear regression be called "machine learning"? Linear regression is definitely an algorithm that can be used in machine learning. But, reductio ad absurdum: Anyone with a copy of Excel can fit a linear model. Even restricting ourselves to linear
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When should linear regression be called "machine learning"?
I think Mitchell's definition provides a helpful way to ground the discussion of machine learning, a sort of first principle. As reproduced on Wikipedia: A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured b...
When should linear regression be called "machine learning"?
I think Mitchell's definition provides a helpful way to ground the discussion of machine learning, a sort of first principle. As reproduced on Wikipedia: A computer program is said to learn from expe
When should linear regression be called "machine learning"? I think Mitchell's definition provides a helpful way to ground the discussion of machine learning, a sort of first principle. As reproduced on Wikipedia: A computer program is said to learn from experience E with respect to some class of tasks T and performan...
When should linear regression be called "machine learning"? I think Mitchell's definition provides a helpful way to ground the discussion of machine learning, a sort of first principle. As reproduced on Wikipedia: A computer program is said to learn from expe
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When should linear regression be called "machine learning"?
There's no law that says that a cabinet maker can't use a barrel maker's saw. Machine learning and statistics are vague labels, but if well-defined there is a lot of overlap between statistics and machine learning. And this goes for methods of these two areas as well as (and separately) for people who label themselves ...
When should linear regression be called "machine learning"?
There's no law that says that a cabinet maker can't use a barrel maker's saw. Machine learning and statistics are vague labels, but if well-defined there is a lot of overlap between statistics and mac
When should linear regression be called "machine learning"? There's no law that says that a cabinet maker can't use a barrel maker's saw. Machine learning and statistics are vague labels, but if well-defined there is a lot of overlap between statistics and machine learning. And this goes for methods of these two areas ...
When should linear regression be called "machine learning"? There's no law that says that a cabinet maker can't use a barrel maker's saw. Machine learning and statistics are vague labels, but if well-defined there is a lot of overlap between statistics and mac
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When should linear regression be called "machine learning"?
Linear regression is a technique, while machine learning is a goal that can be achieved through different means and techniques. So regression performance is measured by how close it fits an expected line/curve, while machine learning is measured by how good it can solve a certain problem, with whatever means necessary.
When should linear regression be called "machine learning"?
Linear regression is a technique, while machine learning is a goal that can be achieved through different means and techniques. So regression performance is measured by how close it fits an expected l
When should linear regression be called "machine learning"? Linear regression is a technique, while machine learning is a goal that can be achieved through different means and techniques. So regression performance is measured by how close it fits an expected line/curve, while machine learning is measured by how good it...
When should linear regression be called "machine learning"? Linear regression is a technique, while machine learning is a goal that can be achieved through different means and techniques. So regression performance is measured by how close it fits an expected l
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When should linear regression be called "machine learning"?
It can be useful to call linear regression machine learning because doing so generally implies a couple important things about how you went about solving your problem: You decided it wasn't necessary to check causal assumptions and prior theory behind your explanatory variables. It signals that your model was not inte...
When should linear regression be called "machine learning"?
It can be useful to call linear regression machine learning because doing so generally implies a couple important things about how you went about solving your problem: You decided it wasn't necessary
When should linear regression be called "machine learning"? It can be useful to call linear regression machine learning because doing so generally implies a couple important things about how you went about solving your problem: You decided it wasn't necessary to check causal assumptions and prior theory behind your ex...
When should linear regression be called "machine learning"? It can be useful to call linear regression machine learning because doing so generally implies a couple important things about how you went about solving your problem: You decided it wasn't necessary
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When should linear regression be called "machine learning"?
Common view is that machine learning made up of 4 areas: 1) Dimensionality Reduction 2) Clustering 3) Classification 4) Regression Linear regression is a regression. Once the model is trained it could be used for predictions, like any other, say, Random Forest Regression.
When should linear regression be called "machine learning"?
Common view is that machine learning made up of 4 areas: 1) Dimensionality Reduction 2) Clustering 3) Classification 4) Regression Linear regression is a regression. Once the model is trained it could
When should linear regression be called "machine learning"? Common view is that machine learning made up of 4 areas: 1) Dimensionality Reduction 2) Clustering 3) Classification 4) Regression Linear regression is a regression. Once the model is trained it could be used for predictions, like any other, say, Random Forest...
When should linear regression be called "machine learning"? Common view is that machine learning made up of 4 areas: 1) Dimensionality Reduction 2) Clustering 3) Classification 4) Regression Linear regression is a regression. Once the model is trained it could
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When should linear regression be called "machine learning"?
I'll argue that the distinction between machine learning and statistical inference is clear. In short, machine learning = prediction of future observations; statistics = explanation. Here is an example from my field of interest (medicine): when developing a drug, we search for gene(s) which best explain a disease state...
When should linear regression be called "machine learning"?
I'll argue that the distinction between machine learning and statistical inference is clear. In short, machine learning = prediction of future observations; statistics = explanation. Here is an exampl
When should linear regression be called "machine learning"? I'll argue that the distinction between machine learning and statistical inference is clear. In short, machine learning = prediction of future observations; statistics = explanation. Here is an example from my field of interest (medicine): when developing a dr...
When should linear regression be called "machine learning"? I'll argue that the distinction between machine learning and statistical inference is clear. In short, machine learning = prediction of future observations; statistics = explanation. Here is an exampl
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When should linear regression be called "machine learning"?
Admittedly, any answer to this question is more opinion than objective fact, but I will try to lay out my logic why I think the answer is never. Any so-called machine learning expert or instructor only reveals their ignorance by representing linear regression as such. Delineation of academic disciplines is more about d...
When should linear regression be called "machine learning"?
Admittedly, any answer to this question is more opinion than objective fact, but I will try to lay out my logic why I think the answer is never. Any so-called machine learning expert or instructor onl
When should linear regression be called "machine learning"? Admittedly, any answer to this question is more opinion than objective fact, but I will try to lay out my logic why I think the answer is never. Any so-called machine learning expert or instructor only reveals their ignorance by representing linear regression ...
When should linear regression be called "machine learning"? Admittedly, any answer to this question is more opinion than objective fact, but I will try to lay out my logic why I think the answer is never. Any so-called machine learning expert or instructor onl
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When should linear regression be called "machine learning"?
It's the Machine, Stupid! I am neither a statistician nor a Big Data(TM) expert. However, I would say that the essential distinction is that "machine learning" requires "a machine". In particular, it implies agency. The result will not be consumed leisurely by a human. Rather, the result will be the input to a clos...
When should linear regression be called "machine learning"?
It's the Machine, Stupid! I am neither a statistician nor a Big Data(TM) expert. However, I would say that the essential distinction is that "machine learning" requires "a machine". In particular, i
When should linear regression be called "machine learning"? It's the Machine, Stupid! I am neither a statistician nor a Big Data(TM) expert. However, I would say that the essential distinction is that "machine learning" requires "a machine". In particular, it implies agency. The result will not be consumed leisurely...
When should linear regression be called "machine learning"? It's the Machine, Stupid! I am neither a statistician nor a Big Data(TM) expert. However, I would say that the essential distinction is that "machine learning" requires "a machine". In particular, i
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When should linear regression be called "machine learning"?
One thing that I need to add (other have made great comments on distinction between ML and Stat) is that on the technical side, many of the classic assumptions of LR does not need to hold for predicting the mean response! Like no body even cares about "homoscedasticity" in ML, or even whether the residuals are normal (...
When should linear regression be called "machine learning"?
One thing that I need to add (other have made great comments on distinction between ML and Stat) is that on the technical side, many of the classic assumptions of LR does not need to hold for predicti
When should linear regression be called "machine learning"? One thing that I need to add (other have made great comments on distinction between ML and Stat) is that on the technical side, many of the classic assumptions of LR does not need to hold for predicting the mean response! Like no body even cares about "homosce...
When should linear regression be called "machine learning"? One thing that I need to add (other have made great comments on distinction between ML and Stat) is that on the technical side, many of the classic assumptions of LR does not need to hold for predicti
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When should linear regression be called "machine learning"?
In my opinion, one can speak of machine learning when a machine is programmed to infer parameters of some model using some data. If a linear regression is done by machine, it therefore qualifies. If done by hand, then it does not. Definitions that hinge on the prevalence of some agent (like Excel), or iterative improve...
When should linear regression be called "machine learning"?
In my opinion, one can speak of machine learning when a machine is programmed to infer parameters of some model using some data. If a linear regression is done by machine, it therefore qualifies. If d
When should linear regression be called "machine learning"? In my opinion, one can speak of machine learning when a machine is programmed to infer parameters of some model using some data. If a linear regression is done by machine, it therefore qualifies. If done by hand, then it does not. Definitions that hinge on the...
When should linear regression be called "machine learning"? In my opinion, one can speak of machine learning when a machine is programmed to infer parameters of some model using some data. If a linear regression is done by machine, it therefore qualifies. If d
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What is the role of the logarithm in Shannon's entropy?
Shannon entropy is a quantity satisfying a set of relations. In short, logarithm is to make it growing linearly with system size and "behaving like information". The first means that entropy of tossing a coin $n$ times is $n$ times entropy of tossing a coin once: $$ - \sum_{i=1}^{2^n} \frac{1}{2^n} \log\left(\tfrac{1}{...
What is the role of the logarithm in Shannon's entropy?
Shannon entropy is a quantity satisfying a set of relations. In short, logarithm is to make it growing linearly with system size and "behaving like information". The first means that entropy of tossin
What is the role of the logarithm in Shannon's entropy? Shannon entropy is a quantity satisfying a set of relations. In short, logarithm is to make it growing linearly with system size and "behaving like information". The first means that entropy of tossing a coin $n$ times is $n$ times entropy of tossing a coin once: ...
What is the role of the logarithm in Shannon's entropy? Shannon entropy is a quantity satisfying a set of relations. In short, logarithm is to make it growing linearly with system size and "behaving like information". The first means that entropy of tossin
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What is the role of the logarithm in Shannon's entropy?
This is the same as the other answers, but I think the best way to explain it is to see what Shannon says in his original paper. The logarithmic measure is more convenient for various reasons: It is practically more useful. Parameters of engineering importance such as time, bandwidth, number of relays, etc., tend to ...
What is the role of the logarithm in Shannon's entropy?
This is the same as the other answers, but I think the best way to explain it is to see what Shannon says in his original paper. The logarithmic measure is more convenient for various reasons: It is
What is the role of the logarithm in Shannon's entropy? This is the same as the other answers, but I think the best way to explain it is to see what Shannon says in his original paper. The logarithmic measure is more convenient for various reasons: It is practically more useful. Parameters of engineering importance s...
What is the role of the logarithm in Shannon's entropy? This is the same as the other answers, but I think the best way to explain it is to see what Shannon says in his original paper. The logarithmic measure is more convenient for various reasons: It is
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What is the role of the logarithm in Shannon's entropy?
another way of looking at this is from an algorithmic point of view. Imagine that you're going to guess a number $x$, that the only information you have is that this number is in the interval $1 \leq x \leq N$. In this situation, the optimal algorithm for guessing the number is a simple Binary search algorithm, which f...
What is the role of the logarithm in Shannon's entropy?
another way of looking at this is from an algorithmic point of view. Imagine that you're going to guess a number $x$, that the only information you have is that this number is in the interval $1 \leq
What is the role of the logarithm in Shannon's entropy? another way of looking at this is from an algorithmic point of view. Imagine that you're going to guess a number $x$, that the only information you have is that this number is in the interval $1 \leq x \leq N$. In this situation, the optimal algorithm for guessing...
What is the role of the logarithm in Shannon's entropy? another way of looking at this is from an algorithmic point of view. Imagine that you're going to guess a number $x$, that the only information you have is that this number is in the interval $1 \leq
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What is the role of the logarithm in Shannon's entropy?
Here's an off-the-cuff explanation. You could say 2 books of the same size have twice as much information as 1 book, right? (Considering a book to be a string of bits.) Well, if a certain outcome has probability P, then you could say its information content is about the number of bits you need to write out 1/P. (e.g. i...
What is the role of the logarithm in Shannon's entropy?
Here's an off-the-cuff explanation. You could say 2 books of the same size have twice as much information as 1 book, right? (Considering a book to be a string of bits.) Well, if a certain outcome has
What is the role of the logarithm in Shannon's entropy? Here's an off-the-cuff explanation. You could say 2 books of the same size have twice as much information as 1 book, right? (Considering a book to be a string of bits.) Well, if a certain outcome has probability P, then you could say its information content is abo...
What is the role of the logarithm in Shannon's entropy? Here's an off-the-cuff explanation. You could say 2 books of the same size have twice as much information as 1 book, right? (Considering a book to be a string of bits.) Well, if a certain outcome has
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What is the role of the logarithm in Shannon's entropy?
The purpose of $\log(p_i)$ appearing in Shannon's Entropy is that $\log(p_i)$ is the only function satisfying the basic set of properties that the entropy function, $H(p_1, \ldots ,p_N)$, is held to embody. Shannon provided a mathematical proof of this result that has been thoroughly picked over and widely accepted. Th...
What is the role of the logarithm in Shannon's entropy?
The purpose of $\log(p_i)$ appearing in Shannon's Entropy is that $\log(p_i)$ is the only function satisfying the basic set of properties that the entropy function, $H(p_1, \ldots ,p_N)$, is held to e
What is the role of the logarithm in Shannon's entropy? The purpose of $\log(p_i)$ appearing in Shannon's Entropy is that $\log(p_i)$ is the only function satisfying the basic set of properties that the entropy function, $H(p_1, \ldots ,p_N)$, is held to embody. Shannon provided a mathematical proof of this result that...
What is the role of the logarithm in Shannon's entropy? The purpose of $\log(p_i)$ appearing in Shannon's Entropy is that $\log(p_i)$ is the only function satisfying the basic set of properties that the entropy function, $H(p_1, \ldots ,p_N)$, is held to e
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What is the role of the logarithm in Shannon's entropy?
Suppose we have a discrete information source that produces symbols from some finite alphabet $\Omega = \{\omega_1, \dotsc, \omega_n\}$ with probabilities $p_1, \dotsc, p_n$. Shannon defines the entropy as the measure $H(p_1, \dotsc, p_n)$ such that $H$ is continuous in its parameters, $H$ is monotone increasing in $n...
What is the role of the logarithm in Shannon's entropy?
Suppose we have a discrete information source that produces symbols from some finite alphabet $\Omega = \{\omega_1, \dotsc, \omega_n\}$ with probabilities $p_1, \dotsc, p_n$. Shannon defines the entro
What is the role of the logarithm in Shannon's entropy? Suppose we have a discrete information source that produces symbols from some finite alphabet $\Omega = \{\omega_1, \dotsc, \omega_n\}$ with probabilities $p_1, \dotsc, p_n$. Shannon defines the entropy as the measure $H(p_1, \dotsc, p_n)$ such that $H$ is contin...
What is the role of the logarithm in Shannon's entropy? Suppose we have a discrete information source that produces symbols from some finite alphabet $\Omega = \{\omega_1, \dotsc, \omega_n\}$ with probabilities $p_1, \dotsc, p_n$. Shannon defines the entro
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What is the role of the logarithm in Shannon's entropy?
Summary: Because it represents average total number of perfect questions that you need them to get answered in order to fully resolve all ambiguities in a data that you hadn't seen yet. A perfect question with $n$ possible answers is one that, when answered, the space of possibilities will be reduced by $n$ times. Exam...
What is the role of the logarithm in Shannon's entropy?
Summary: Because it represents average total number of perfect questions that you need them to get answered in order to fully resolve all ambiguities in a data that you hadn't seen yet. A perfect ques
What is the role of the logarithm in Shannon's entropy? Summary: Because it represents average total number of perfect questions that you need them to get answered in order to fully resolve all ambiguities in a data that you hadn't seen yet. A perfect question with $n$ possible answers is one that, when answered, the s...
What is the role of the logarithm in Shannon's entropy? Summary: Because it represents average total number of perfect questions that you need them to get answered in order to fully resolve all ambiguities in a data that you hadn't seen yet. A perfect ques
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What is the role of the logarithm in Shannon's entropy?
This question was raised two years ago and there have been many awesome answers already, but I'd like to add mine which helped myself a lot. The question is What purpose does the logarithm serve in this equation? The logarithm(usually based on 2) is because of the Kraft's Inequality. $\sum_{i=1}^m 2^{-l_i} <= 1$ w...
What is the role of the logarithm in Shannon's entropy?
This question was raised two years ago and there have been many awesome answers already, but I'd like to add mine which helped myself a lot. The question is What purpose does the logarithm serve in
What is the role of the logarithm in Shannon's entropy? This question was raised two years ago and there have been many awesome answers already, but I'd like to add mine which helped myself a lot. The question is What purpose does the logarithm serve in this equation? The logarithm(usually based on 2) is because of...
What is the role of the logarithm in Shannon's entropy? This question was raised two years ago and there have been many awesome answers already, but I'd like to add mine which helped myself a lot. The question is What purpose does the logarithm serve in
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What is the role of the logarithm in Shannon's entropy?
A historical view may be interesting. Entropy is related to the concept of weight of evidence from information theory (note this is not the same as discussed here Intuition behind Weight of Evidence and Information Value formula) This $\text{woe}$ is discussed deeply in this book by IJ Good, (much of the content in tha...
What is the role of the logarithm in Shannon's entropy?
A historical view may be interesting. Entropy is related to the concept of weight of evidence from information theory (note this is not the same as discussed here Intuition behind Weight of Evidence a
What is the role of the logarithm in Shannon's entropy? A historical view may be interesting. Entropy is related to the concept of weight of evidence from information theory (note this is not the same as discussed here Intuition behind Weight of Evidence and Information Value formula) This $\text{woe}$ is discussed dee...
What is the role of the logarithm in Shannon's entropy? A historical view may be interesting. Entropy is related to the concept of weight of evidence from information theory (note this is not the same as discussed here Intuition behind Weight of Evidence a
1,591
What is the role of the logarithm in Shannon's entropy?
I don't think it is possible to give you a universal "intuitive" answer. I'll give you answer that is intuitive for some people, such as physicists. Logarithm is there to get the average energy of the system. Here's details. Shannon used a word "entropy" because he adapted the concept from statistical mechanics. In sta...
What is the role of the logarithm in Shannon's entropy?
I don't think it is possible to give you a universal "intuitive" answer. I'll give you answer that is intuitive for some people, such as physicists. Logarithm is there to get the average energy of the
What is the role of the logarithm in Shannon's entropy? I don't think it is possible to give you a universal "intuitive" answer. I'll give you answer that is intuitive for some people, such as physicists. Logarithm is there to get the average energy of the system. Here's details. Shannon used a word "entropy" because h...
What is the role of the logarithm in Shannon's entropy? I don't think it is possible to give you a universal "intuitive" answer. I'll give you answer that is intuitive for some people, such as physicists. Logarithm is there to get the average energy of the
1,592
What is the role of the logarithm in Shannon's entropy?
Entropy is defined as the logarithm of the geometric mean of the multinomial coefficient that expresses the number of states a system can be in: $$\log \sqrt[N]{N \choose n_1,\ldots,n_k}$$ The logarithms appear in the formula after using Stirling's approximation of the factorial (see this explanation)
What is the role of the logarithm in Shannon's entropy?
Entropy is defined as the logarithm of the geometric mean of the multinomial coefficient that expresses the number of states a system can be in: $$\log \sqrt[N]{N \choose n_1,\ldots,n_k}$$ The logarit
What is the role of the logarithm in Shannon's entropy? Entropy is defined as the logarithm of the geometric mean of the multinomial coefficient that expresses the number of states a system can be in: $$\log \sqrt[N]{N \choose n_1,\ldots,n_k}$$ The logarithms appear in the formula after using Stirling's approximation o...
What is the role of the logarithm in Shannon's entropy? Entropy is defined as the logarithm of the geometric mean of the multinomial coefficient that expresses the number of states a system can be in: $$\log \sqrt[N]{N \choose n_1,\ldots,n_k}$$ The logarit
1,593
What is the role of the logarithm in Shannon's entropy?
Based on your nonacceptance of any already answers, I think what you are looking for is the reason why Shannon used logarithm in his formula at the first place. In other words, the philosophy of it. Disclaimer: I'm just into this field for a week, coming here because of having the question just like you. If you have mo...
What is the role of the logarithm in Shannon's entropy?
Based on your nonacceptance of any already answers, I think what you are looking for is the reason why Shannon used logarithm in his formula at the first place. In other words, the philosophy of it. D
What is the role of the logarithm in Shannon's entropy? Based on your nonacceptance of any already answers, I think what you are looking for is the reason why Shannon used logarithm in his formula at the first place. In other words, the philosophy of it. Disclaimer: I'm just into this field for a week, coming here beca...
What is the role of the logarithm in Shannon's entropy? Based on your nonacceptance of any already answers, I think what you are looking for is the reason why Shannon used logarithm in his formula at the first place. In other words, the philosophy of it. D
1,594
What is the role of the logarithm in Shannon's entropy?
The log comes from the derivation of a function H satisfying certain natural requirements. See pg. 3 Sec. 2 of this source: http://www.lptl.jussieu.fr/user/lesne/MSCS-entropy.pdf Given the axioms, if you carry out the optimization, you get a unique (upto constants) function with a log in it. All of the above answers ar...
What is the role of the logarithm in Shannon's entropy?
The log comes from the derivation of a function H satisfying certain natural requirements. See pg. 3 Sec. 2 of this source: http://www.lptl.jussieu.fr/user/lesne/MSCS-entropy.pdf Given the axioms, if
What is the role of the logarithm in Shannon's entropy? The log comes from the derivation of a function H satisfying certain natural requirements. See pg. 3 Sec. 2 of this source: http://www.lptl.jussieu.fr/user/lesne/MSCS-entropy.pdf Given the axioms, if you carry out the optimization, you get a unique (upto constants...
What is the role of the logarithm in Shannon's entropy? The log comes from the derivation of a function H satisfying certain natural requirements. See pg. 3 Sec. 2 of this source: http://www.lptl.jussieu.fr/user/lesne/MSCS-entropy.pdf Given the axioms, if
1,595
What is the role of the logarithm in Shannon's entropy?
I guess your question is more about the "meaning" of that logarithm and why each component contributes to the overall meaning of the formula, rather than the mere formalism showing the coherence of the definition to certain requirements. The idea in the Shannon entropy is to evaluate the information of a message by loo...
What is the role of the logarithm in Shannon's entropy?
I guess your question is more about the "meaning" of that logarithm and why each component contributes to the overall meaning of the formula, rather than the mere formalism showing the coherence of th
What is the role of the logarithm in Shannon's entropy? I guess your question is more about the "meaning" of that logarithm and why each component contributes to the overall meaning of the formula, rather than the mere formalism showing the coherence of the definition to certain requirements. The idea in the Shannon en...
What is the role of the logarithm in Shannon's entropy? I guess your question is more about the "meaning" of that logarithm and why each component contributes to the overall meaning of the formula, rather than the mere formalism showing the coherence of th
1,596
What is the role of the logarithm in Shannon's entropy?
There is a profound reason why the logarithm comes into picture, and it is not randomly chosen. The relationship between $\log$ and information stems from this simple way of writing any number $m$ (the symbols don't have any meaning yet), and the discussion that follows. $$ m = \frac{1}{p} = 2^{i} \tag{1}$$ The above t...
What is the role of the logarithm in Shannon's entropy?
There is a profound reason why the logarithm comes into picture, and it is not randomly chosen. The relationship between $\log$ and information stems from this simple way of writing any number $m$ (th
What is the role of the logarithm in Shannon's entropy? There is a profound reason why the logarithm comes into picture, and it is not randomly chosen. The relationship between $\log$ and information stems from this simple way of writing any number $m$ (the symbols don't have any meaning yet), and the discussion that f...
What is the role of the logarithm in Shannon's entropy? There is a profound reason why the logarithm comes into picture, and it is not randomly chosen. The relationship between $\log$ and information stems from this simple way of writing any number $m$ (th
1,597
What is the role of the logarithm in Shannon's entropy?
Ok, no maths. I too was curious to know the same thing, and have understood the purpose served by using logarithm in entropy equation?. Let's use a simple example. Suppose we are looking at 3 different containers. Each container has some triangles or circles. Let's focus on first container - Container 1 which has 26 t...
What is the role of the logarithm in Shannon's entropy?
Ok, no maths. I too was curious to know the same thing, and have understood the purpose served by using logarithm in entropy equation?. Let's use a simple example. Suppose we are looking at 3 differen
What is the role of the logarithm in Shannon's entropy? Ok, no maths. I too was curious to know the same thing, and have understood the purpose served by using logarithm in entropy equation?. Let's use a simple example. Suppose we are looking at 3 different containers. Each container has some triangles or circles. Let...
What is the role of the logarithm in Shannon's entropy? Ok, no maths. I too was curious to know the same thing, and have understood the purpose served by using logarithm in entropy equation?. Let's use a simple example. Suppose we are looking at 3 differen
1,598
What is the role of the logarithm in Shannon's entropy?
Entropy measures how chaotic and unpredictable is given distribution. For distributions with low entropy certain values occur significantly more often than others. When we draw a sample, the probability density function tells us how surprised are we about the given outcome. Let's draw a sequence of $N$ independent samp...
What is the role of the logarithm in Shannon's entropy?
Entropy measures how chaotic and unpredictable is given distribution. For distributions with low entropy certain values occur significantly more often than others. When we draw a sample, the probabili
What is the role of the logarithm in Shannon's entropy? Entropy measures how chaotic and unpredictable is given distribution. For distributions with low entropy certain values occur significantly more often than others. When we draw a sample, the probability density function tells us how surprised are we about the give...
What is the role of the logarithm in Shannon's entropy? Entropy measures how chaotic and unpredictable is given distribution. For distributions with low entropy certain values occur significantly more often than others. When we draw a sample, the probabili
1,599
Validation Error less than training error?
It is difficult to be certain without knowing your actual methodology (e.g. cross-validation method, performance metric, data splitting method, etc.). Generally speaking though, training error will almost always underestimate your validation error. However it is possible for the validation error to be less than the tr...
Validation Error less than training error?
It is difficult to be certain without knowing your actual methodology (e.g. cross-validation method, performance metric, data splitting method, etc.). Generally speaking though, training error will al
Validation Error less than training error? It is difficult to be certain without knowing your actual methodology (e.g. cross-validation method, performance metric, data splitting method, etc.). Generally speaking though, training error will almost always underestimate your validation error. However it is possible for ...
Validation Error less than training error? It is difficult to be certain without knowing your actual methodology (e.g. cross-validation method, performance metric, data splitting method, etc.). Generally speaking though, training error will al
1,600
Validation Error less than training error?
One possibility: If you are using dropout regularization layer in your network, it is reasonable that the validation error is smaller than training error. Because usually dropout is activated when training but deactivated when evaluating on the validation set. You get a more smooth (usually means better) function in th...
Validation Error less than training error?
One possibility: If you are using dropout regularization layer in your network, it is reasonable that the validation error is smaller than training error. Because usually dropout is activated when tra
Validation Error less than training error? One possibility: If you are using dropout regularization layer in your network, it is reasonable that the validation error is smaller than training error. Because usually dropout is activated when training but deactivated when evaluating on the validation set. You get a more s...
Validation Error less than training error? One possibility: If you are using dropout regularization layer in your network, it is reasonable that the validation error is smaller than training error. Because usually dropout is activated when tra