cat(rep('=', 80), '\n\n', 'OUTPUT FROM: shorts/06_analysis_multipletesting.R', '\n\n', sep = '' ) library(data.table) library(car) library(sandwich) library(lmtest) library(ggplot2) library(tidyverse) ############### ## functions ## ############### `%.%` <- paste0 simes <- function(ps){ min(sort(length(ps) * ps / rank(ps))) } ### functions to handle inconsistent interaction ordering of mlm() ### ## convert interaction terms of form 'b#:a#' to 'a#:b#' reorder.interaction.names <- function(x, prefix = ''){ x <- gsub('^' %.% prefix, '', x) sapply(strsplit(x, ':'), function(y){ paste(sort(y), collapse = ':') }) } ## take term of form 'a1:b1', look up in vector of form 'b#:a#, return 'b1:a1' convert.interaction.names <- function(x, y, prefix.y = ''){ ind <- match(reorder.interaction.names(x), reorder.interaction.names(y, prefix = prefix.y) ) return(y[ind]) } ## modified from print.linearHypothesis.mlm to use alternate df & return pvals ## (print method is responsible for doing the actual computation of pvals) extract.lht <- function(x, SSP = TRUE, SSPE = SSP, digits = getOption('digits'), df.residual = x$df.residual ){ test <- x$test if (!is.null(x$P) && SSP) { P <- x$P cat("\n Response transformation matrix:\n") attr(P, "assign") <- NULL attr(P, "contrasts") <- NULL print(P, digits = digits) } if (SSP) { cat("\nSum of squares and products for the hypothesis:\n") print(x$SSPH, digits = digits) } if (SSPE) { cat("\nSum of squares and products for error:\n") print(x$SSPE, digits = digits) } if ((!is.null(x$singular)) && x$singular) { warning("the error SSP matrix is singular; multivariate tests are unavailable") return(invisible(x)) } SSPE.qr <- qr(x$SSPE) eigs <- Re(eigen(qr.coef(SSPE.qr, x$SSPH), symmetric = FALSE)$values) tests <- matrix(NA, 4, 4) rownames(tests) <- c("Pillai", "Wilks", "Hotelling-Lawley", "Roy") if ("Pillai" %in% test) tests[1, 1:4] <- car:::Pillai(eigs, x$df, df.residual) if ("Wilks" %in% test) tests[2, 1:4] <- car:::Wilks(eigs, x$df, df.residual) if ("Hotelling-Lawley" %in% test) tests[3, 1:4] <- car:::HL(eigs, x$df, df.residual) if ("Roy" %in% test) tests[4, 1:4] <- car:::Roy(eigs, x$df, df.residual) tests <- na.omit(tests) ok <- tests[, 2] >= 0 & tests[, 3] > 0 & tests[, 4] > 0 ok <- !is.na(ok) & ok tests <- cbind(x$df, tests, pf(tests[ok, 2], tests[ok, 3], tests[ok, 4], lower.tail = FALSE)) colnames(tests) <- c("Df", "test stat", "approx F", "num Df", "den Df", "Pr(>F)") tests <- structure(as.data.frame(tests), heading = paste("\nMultivariate Test", if (nrow(tests) > 1) "s", ": ", x$title, sep = ""), class = c("anova", "data.frame" ) ) return(tests) } ############### ## load data ## ############### d <- fread('../results/intermediate data/shorts/qualtrics_w12_clean_ytrecs_may2024.csv') ############## ## controls ## ############## platform.controls <- c('age_cat', 'male', 'pol_interest', 'freq_youtube') mwpolicy.controls <- 'mw_index_pre' media.controls <- c('trust_majornews', 'trust_youtube', 'fabricate_majornews', 'fabricate_youtube') affpol.controls <- c('affpol_smart', 'affpol_comfort') controls.raw <- unique(c(platform.controls, mwpolicy.controls, media.controls, affpol.controls)) ## transform control variables by creating dummies and demeaning controls.trans <- list() for (j in controls.raw){ ## convert to dummies if needed controls.j <- model.matrix(as.formula('~ 0 + ' %.% j), model.frame(as.formula('~ 0 + ' %.% j), data = d, na.action = 'na.pass' ) ) ## demean by column controls.j <- sweep(controls.j, MARGIN = 2, STATS = colMeans(controls.j, na.rm = TRUE), FUN = `-`, ) colnames(controls.j) <- make.names(colnames(controls.j)) ## remove control from original data d[[j]] <- NULL ## reinsert transformed control d <- cbind(d, controls.j) ## keep track of which original controls map to which transformed controls controls.trans[[j]] <- colnames(controls.j) } ## map original control variables to transformed versions platform.controls <- unlist(controls.trans[platform.controls]) mwpolicy.controls <- unlist(controls.trans[mwpolicy.controls]) media.controls <- unlist(controls.trans[media.controls]) affpol.controls <- unlist(controls.trans[affpol.controls]) ### Platform interactions ### d <- d %>% filter(!is.na(interface_duration)) # -- 929 observations ############## ## outcomes ## ############## ### HYPOTHESIS FAMILY: MIN WAGE POLICY ATTITUDES ### ## ONLY HAVE ONE OUTCOME mwpolicy.outcomes <- 'mw_index' outcomes <- unique(c(mwpolicy.outcomes)) ################ ## treatments ## ################ ## CREATE ATTITUDE DUMMIES # 1-LIBERALS, 2-MODERATES, 3-CONSERVATIVES d[, attitude := c('pro', 'neutral', 'anti')[thirds]] d[, attitude.pro := as.numeric(attitude == 'pro')] d[, attitude.neutral := as.numeric(attitude == 'neutral')] d[, attitude.anti := as.numeric(attitude == 'anti')] ## CREATE SEQUENCE DUMMIES -- AC, PC, AI, PI d[, recsys.ac := as.numeric(treatment_arm %like% 'ac')] d[, recsys.pc := as.numeric(treatment_arm %like% 'pc')] d[, recsys.ai := as.numeric(treatment_arm %like% 'ai')] d[, recsys.pi := as.numeric(treatment_arm %like% 'pi')] # (a) Increasing vs. Constant assignment among Pro participants; # (b) Increasing vs. Constant assignment among Anti participants; # (c) Increasing vs. Constant assignment among Moderate participants assigned to a Prosequence; # (d) Increasing vs. Constant assignment among moderate participants assigned to an Antisequence; # (e) Pro vs. Anti sequence assignment among moderate participants with Increasing assignment; # (f) Pro vs. Anti seed among moderate participants with Constant assignment. # Treatments: treatments <- c('attitude.pro:recsys.pi', # (a) 'attitude.pro:recsys.pc', # (a) 'attitude.anti:recsys.ai', # (b) 'attitude.anti:recsys.ac', # (b) 'attitude.neutral:recsys.ai', # (d-e) 'attitude.neutral:recsys.pi', # (c-e) 'attitude.neutral:recsys.ac', # (d-f) 'attitude.neutral:recsys.pc') # (c-f) # Contrasts: contrasts <- rbind( # Increasing vs. Constant assignment among Pro participants i = c(treat = 'attitude.pro:recsys.pi', ctrl = 'attitude.pro:recsys.pc' ), # Increasing vs. Constant assignment among Anti participants ii = c(treat = 'attitude.anti:recsys.ai', ctrl = 'attitude.anti:recsys.ac' ), # Increasing vs. Constant assignment among Moderate participants assigned to a Pro sequence iii = c(treat = 'attitude.neutral:recsys.pi', ctrl = 'attitude.neutral:recsys.pc' ), # Increasing vs. Constant assignment among moderate participants assigned to an Anti sequence iv = c(treat = 'attitude.neutral:recsys.ai', ctrl = 'attitude.neutral:recsys.ac' ), # Pro vs. Anti sequence assignment among moderate participants with Increasing assignment v = c(treat = 'attitude.neutral:recsys.ai', ctrl = 'attitude.neutral:recsys.pi' ), # Pro vs. Anti sequence assignment among moderate participants with Constant assignment vi = c(treat = 'attitude.neutral:recsys.ac', ctrl = 'attitude.neutral:recsys.pc' ) ) ########################## ## hierarchical testing ## ########################## ## initialize top layer p-values: ## does treatment have any effect on any outcome in family families <- c('mwpolicy') layer1.pvals <- rep(NA_real_, length(families)) layer1.notes <- rep('', length(families)) names(layer1.pvals) <- families ## initialize 2nd layer p-values: ## which treatment has detectable effect? contrast.pvals <- rep(NA_real_, nrow(contrasts)) names(contrast.pvals) <- paste(contrasts[, 'treat'], contrasts[, 'ctrl'], sep = '.vs.' ) layer2.pvals <- list( mwpolicy = contrast.pvals) rm(contrast.pvals) ## initialize 3rd layer p-values: ## on which specific outcome in family? layer3.pvals <- list() layer3.ests <- list() layer3.ses <- list() layer3.notes <- list() for (i in 1:length(families)){ family <- families[i] layer3.pvals[[family]] <- list() layer3.ests[[family]] <- list() layer3.ses[[family]] <- list() layer3.notes[[family]] <- list() outcomes <- get(family %.% '.outcomes') for (j in 1:nrow(contrasts)){ contrast <- paste(contrasts[j, 'treat'], contrasts[j, 'ctrl'], sep = '.vs.' ) layer3.pvals[[family]][[contrast]] <- numeric(0) layer3.ests[[family]][[contrast]] <- numeric(0) layer3.ses[[family]][[contrast]] <- numeric(0) for (k in 1:length(outcomes)){ outcome <- outcomes[k] layer3.pvals[[family]][[contrast]][outcome] <- NA_real_ layer3.ests[[family]][[contrast]][outcome] <- NA_real_ layer3.ses[[family]][[contrast]][outcome] <- NA_real_ layer3.notes[[family]][outcome] <- '' } } } ### begin nested analyses ### for (i in 1:length(families)){ family <- families[i] family.outcomes <- get(family %.% '.outcomes') family.controls <- get(family %.% '.controls') family.controls.interactions <- as.character( outer(treatments, family.controls, FUN = function(x, y) x %.% ':' %.% y ) ) family.formula <- 'cbind(' %.% # outcomes paste(family.outcomes, collapse = ', ' ) %.% ') ~\n0 +\n' %.% paste(treatments, # treatments (base terms) collapse = ' +\n' ) %.% ' +\n' %.% paste(family.controls, # controls (base terms) collapse = ' +\n' )## %.% ' +\n' %.% ## paste( # treat-ctrl interactions ## family.controls.interactions, ## collapse = ' +\n' ## ) cat(rep('=', 80), '\n\nHYPOTHESIS FAMILY: ', family, '\n\nrunning mlm:\n\n', family.formula, '\n\n', sep = '' ) ## run model family.mod <- lm(family.formula, d) ## hack to eliminate NA coefs if (any(is.na(coef(family.mod)))){ if ('mlm' %in% class(family.mod)){ drop <- rownames(coef(family.mod))[is.na(coef(family.mod))[, 1]] } else { drop <- names(coef(family.mod))[is.na(coef(family.mod))] } drop <- convert.interaction.names(drop, c(family.controls, family.controls.interactions ) ) layer1.notes[[i]] <- layer1.notes[[i]] %.% 'dropped the following coefs: ' %.% paste(drop, sep = ', ') %.% '\n\n' family.formula <- gsub( '\\s+\\+\\s+(' %.% paste(drop, collapse = '|') %.% ')', '', family.formula ) family.mod <- lm(family.formula, d) } family.vcov <- vcovHC(family.mod) if (is.null(dim(coef(family.mod)))){ coef.names <- names(coef(family.mod)) } else { coef.names <- rownames(coef(family.mod)) } ### top layer: test overall significance of all contrasts on all outcomes ### ## convert interaction terms to whatever mlm() named it treats <- convert.interaction.names(contrasts[, 'treat'], coef.names) ctrls <- convert.interaction.names(contrasts[, 'ctrl'], coef.names) ## test jointly lht.attempt <- tryCatch({ if ('mlm' %in% class(family.mod)){ contrast.lht <- linearHypothesis( family.mod, vcov. = family.vcov, hypothesis.matrix = sprintf('%s - %s', treats, ctrls), rhs = matrix(0, nrow = nrow(contrasts), ncol = length(family.outcomes)), test = 'Pillai' ) layer1.pvals[[i]] <- extract.lht(contrast.lht)[, 'Pr(>F)'] } else { contrast.lht <- linearHypothesis( family.mod, vcov. = family.vcov, hypothesis.matrix = sprintf('%s - %s', treats, ctrls), rhs = matrix(0, nrow = nrow(contrasts), ncol = length(family.outcomes)), test = 'F' ) layer1.pvals[[i]] <- contrast.lht[['Pr(>F)']][2] } }, error = function(e){ warning(sprintf('caught error in %s family:', family), e) ## return error as string for inclusion in notes 'caught error: ' %.% e %.% '\n\n' }) if (lht.attempt %like% 'caught error'){ layer1.notes[[i]] <- layer1.notes[[i]] %.% lht.attempt } ### layer 2: test each contrast individually on all outcomes ### for (j in 1:nrow(contrasts)){ ## test group equality on all outcomes if ('mlm' %in% class(family.mod)){ contrast.lht <- linearHypothesis( family.mod, vcov. = family.vcov, hypothesis.matrix = sprintf('%s - %s', treats[j], ctrls[j]), rhs = matrix(0, nrow = 1, ncol = length(family.outcomes)), test = 'Pillai' ) layer2.pvals[[i]][j] <- extract.lht(contrast.lht)[, 'Pr(>F)'] } else { contrast.lht <- linearHypothesis( family.mod, vcov. = family.vcov, hypothesis.matrix = sprintf('%s - %s', treats[j], ctrls[j]), rhs = matrix(0, nrow = 1, ncol = length(family.outcomes)), test = 'F' ) layer2.pvals[[i]][j] <- contrast.lht[['Pr(>F)']][2] } } ### layer 3: test each contrast on each outcome individually ### for (k in 1:length(family.outcomes)){ outcome <- family.outcomes[k] outcome.formula <- outcome %.% ' ~\n0 +\n' %.% paste(treatments, # treatments (base terms) collapse = ' +\n' ) %.% ' +\n' %.% paste(family.controls, # controls (base terms) collapse = ' +\n' )## %.% ' +\n' %.% ## paste( # treat-ctrl interactions ## family.controls.interactions, ## collapse = ' +\n' ## ) cat(rep('-', 40), '\n\nrunning lm:\n\n', outcome.formula, '\n\n', sep = '') outcome.mod <- lm(outcome.formula, d) ## hack to eliminate NA coefs if (any(is.na(coef(outcome.mod)))){ drop <- names(coef(outcome.mod))[is.na(coef(outcome.mod))] drop <- convert.interaction.names(drop, c(family.controls, family.controls.interactions ) ) layer3.notes[[i]][k] <- layer3.notes[[i]][k] %.% 'dropped the following coefs: ' %.% paste(drop, sep = ', ') %.% '\n\n' outcome.formula <- gsub( '\\s+\\+\\s+(' %.% paste(drop, collapse = '|') %.% ')', '', outcome.formula ) outcome.mod <- lm(outcome.formula, d) } outcome.vcov <- vcovHC(outcome.mod) if (any(!is.finite(outcome.vcov))){ outcome.vcov <- vcov(outcome.mod) layer3.notes[[i]][k] <- layer3.notes[[i]][k] %.% 'falling back to non-robust vcov\n\n' } coef.names <- names(coef(outcome.mod)) for (j in 1:nrow(contrasts)){ ## convert this interaction term to whatever llm() named it treat <- convert.interaction.names(contrasts[j, 'treat'], coef.names) ctrl <- convert.interaction.names(contrasts[j, 'ctrl'], coef.names) ## test group equality on this outcome contrast.lht <- linearHypothesis( outcome.mod, vcov. = outcome.vcov, hypothesis.matrix = sprintf('%s - %s', treat, ctrl), test = 'F' ) layer3.pvals[[i]][[j]][k] <- contrast.lht[['Pr(>F)']][2] layer3.ests[[i]][[j]][k] <- ( coef(outcome.mod)[treat] - coef(outcome.mod)[ctrl] ) ## * attr(d[[outcome]], 'scaled:scale') # note: uncomment if rescaling layer3.ses[[i]][[j]][k] <- sqrt( outcome.vcov[treat, treat] + outcome.vcov[ctrl, ctrl] - 2 * outcome.vcov[treat, ctrl] ) } } } ################################# ## multiple testing correction ## ################################# thresh <- .05 ## if layer-1 f-test is infeasible for a family due to collinearity, ## obtain layer-1 p-values for that family by simes for (i in which(is.na(layer1.pvals))){ layer1.pvals[i] <- simes(layer2.pvals[[i]]) } ## multiple testing adjustment for layer 1 layer1.pvals.adj <- p.adjust(layer1.pvals, 'BH') layer1.nonnull.prop <- mean(layer1.pvals.adj < thresh) ## test layer-2 hypotheses only if layer 1 passes layer2.pvals.adj <- layer2.pvals # start by copying unadjusted layer-2 p-values layer2.nonnull.prop <- rep(NA, length(layer1.pvals.adj)) names(layer2.nonnull.prop) <- names(layer1.pvals.adj) for (i in 1:length(layer1.pvals)){ if (layer1.pvals.adj[i] < thresh){ # if layer 1 passes ## adjust for multiplicity within layer 2... layer2.pvals.adj[[i]] <- p.adjust(layer2.pvals[[i]], 'BH') ## ... and inflate to account for selection at layer 1 layer2.pvals.adj[[i]] <- pmin(layer2.pvals.adj[[i]] / layer1.nonnull.prop, 1) ## keep track of selection at layer 2 for use in layer 3 layer2.nonnull.prop[i] <- mean(layer2.pvals.adj[[i]] < thresh) } else { # if layer 1 fails layer2.pvals.adj[[i]] <- rep(NA_real_, length(layer2.pvals[[i]])) names(layer2.pvals.adj[[i]]) <- names(layer2.pvals[[i]]) } } ## test layer-3 hypotheses only if layers 1 & 2 pass layer3.pvals.adj <- layer3.pvals # start by copying unadjusted layer-3 p-values for (i in 1:length(layer1.pvals.adj)){ for (j in 1:length(layer2.pvals.adj[[i]])){ ## if (layer1.pvals.adj[i] < thresh && # if layer 1 passes... layer2.pvals.adj[[i]][j] < thresh # ... and if layer 2 passes ){ ## adjust for multiplicity within layer 3... layer3.pvals.adj[[i]][[j]] <- p.adjust(layer3.pvals[[i]][[j]], 'BH') ## ... and inflate to account for selection at layer 1 layer3.pvals.adj[[i]][[j]] <- pmin( layer3.pvals.adj[[i]][[j]] / layer1.nonnull.prop / layer2.nonnull.prop[i], 1 ) } else { layer3.pvals.adj[[i]][[j]] <- rep(NA_real_, length(layer3.pvals[[i]][[j]])) names(layer3.pvals.adj[[i]][[j]]) <- names(layer3.pvals[[i]][[j]]) } } } pvals.adj <- data.table(layer1 = character(0), layer2 = character(0), layer3 = character(0), p.adj = numeric(0), est = numeric(0), se = numeric(0) ) for (i in 1:length(layer1.pvals.adj)){ pvals.adj <- rbind(pvals.adj, data.table(layer1 = names(layer1.pvals.adj)[i], layer2 = 'overall', layer3 = 'overall', p.adj = layer1.pvals.adj[i], est = NA_real_, se = NA_real_ ) ) for (j in 1:length(layer2.pvals.adj[[i]])){ pvals.adj <- rbind(pvals.adj, data.table(layer1 = names(layer1.pvals.adj)[i], layer2 = names(layer2.pvals.adj[[i]])[j], layer3 = 'overall', p.adj = layer2.pvals.adj[[i]][j], est = NA_real_, se = NA_real_ ) ) for (k in 1:length(layer3.pvals.adj[[i]][[j]])){ pvals.adj <- rbind(pvals.adj, data.table(layer1 = names(layer1.pvals.adj)[i], layer2 = names(layer2.pvals.adj[[i]])[j], layer3 = names(layer3.pvals.adj[[i]][[j]])[k], p.adj = layer3.pvals.adj[[i]][[j]][k], est = layer3.ests[[i]][[j]][k], se = layer3.ses[[i]][[j]][k] ) ) } } } ## write out fwrite(pvals.adj, '../results/padj_basecontrol_may2024.csv') ## prettify for reading pvals.adj.pretty <- pvals.adj colnames(pvals.adj.pretty) <- gsub('layer1', 'layer1_hypothesisfamily', colnames(pvals.adj.pretty) ) colnames(pvals.adj.pretty) <- gsub('layer2', 'layer2_treatmentcontrast', colnames(pvals.adj.pretty) ) colnames(pvals.adj.pretty) <- gsub('layer3', 'layer3_specificoutcome', colnames(pvals.adj.pretty) ) pvals.adj.pretty[, layer2_treatmentcontrast := gsub( 'attitude\\.(pro|anti|neutral)(:assg\\.(inc|cons))?:recsys.(ca|cp|ip|ia)', '\\1 \\3 \\4', layer2_treatmentcontrast )] pvals.adj.pretty[, layer2_treatmentcontrast := gsub( '.vs.', ' - ', layer2_treatmentcontrast, fixed = TRUE )] pvals.adj.pretty[, layer2_treatmentcontrast := gsub( ' +', ' ', layer2_treatmentcontrast )] fwrite(pvals.adj.pretty, '../results/padj_basecontrol_pretty_ytrecs_may2024.csv' ) # pvals.adj.pretty[p.adj < .05 & layer3_specificoutcome != 'overall',] ################################ ######### OMNIBUS TEST ######### ################################ # Step 1: Create a binary variable indicating increasing condition d$is_increasing <- ifelse(d$treatment_arm == "pi" | d$treatment_arm == "ai", 1, 0) # Step 2: Reverse values for individuals in the Pro condition d$mw_index_pre[d$treatment_arm %like% "pi|pc"] <- 1 - d$mw_index_pre[d$treatment_arm %like% "pi|pc"] d$mw_index[d$treatment_arm %like% "pi|pc"] <- 1 - d$mw_index[d$treatment_arm %like% "pi|pc"] # Step 3: Perform the linear regression (omnibus test) model <- lm(I(mw_index - mw_index_pre) ~ is_increasing, data = d) # View the summary of the model summary(model) rm(list = ls())