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Code used to do the simulations explained on my paper.
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| ##### here I re-run Bollen & Paxton's regressions, but with simulated factor scores | |
| library(MASS) | |
| library(sem) | |
| setwd(basedir) | |
| bolpaxdata <- read.csv("~/Desktop/SCpaper/bollenpaxtondata.csv") # change path as needed | |
| set.seed(10101957) # set seed to make exercise replicable | |
| ##### part 0: preliminary stuff (transform variables, specify CFA model, create subroutines) | |
| ### transform variables | |
| bolpaxdata$coverage <- bolpaxdata$nyt + bolpaxdata$vanderbilt + bolpaxdata$facts | |
| bolpaxdata$age <- 1980 - bolpaxdata$independence | |
| bolpaxdata$coups <- bolpaxdata$coups76 + bolpaxdata$coups77 + bolpaxdata$coups78 + bolpaxdata$coups79 + bolpaxdata$coups80 | |
| bolpaxdata$radiostvs <- bolpaxdata$radios + bolpaxdata$tvs | |
| bolpaxdata$coverage[bolpaxdata$coverage==0] <- .001 | |
| bolpaxdata$age[bolpaxdata$age<1] <- NA | |
| bolpaxdata$lcoverage <- log(bolpaxdata$coverage) | |
| bolpaxdata$lage <- log(bolpaxdata$age) | |
| bolpaxdata$lradiostvs <- log(bolpaxdata$radiostvs) | |
| bolpaxdata$lpopulation <- log(bolpaxdata$population) | |
| bolpaxdata$larea <- log(bolpaxdata$area) | |
| bolpaxdata$lenergy <- log(bolpaxdata$energy) | |
| bolpaxdata$lprotests <- log(bolpaxdata$protests) | |
| bolpaxdata$lstrikes <- log(bolpaxdata$strikes) | |
| bolpaxdata$lriots <- log(bolpaxdata$riots) | |
| ### specify CFA model | |
| model.cfadata <- specifyModel(quiet=TRUE) | |
| edemoc -> indicator1, lambda_edemoc_indicator1, 69.87 | |
| edemoc -> indicator2, lambda_edemoc_indicator2, 68.57 | |
| edemoc -> indicator3, lambda_edemoc_indicator3, 53.45 | |
| edemoc -> indicator4, lambda_edemoc_indicator4, 28.21 | |
| edemoc -> indicator5, lambda_edemoc_indicator5, 40.63 | |
| edemoc -> indicator6, lambda_edemoc_indicator6, 97.69 | |
| edemoc -> indicator7, lambda_edemoc_indicator7, 21.17 | |
| edemoc -> indicator8, lambda_edemoc_indicator8, 51.63 | |
| edemoc -> indicator9, lambda_edemoc_indicator9, 26.09 | |
| edemoc -> indicator10, lambda_edemoc_indicator10, 55.01 | |
| edemoc -> indicator11, lambda_edemoc_indicator11, 63.13 | |
| edemoc -> indicator12, lambda_edemoc_indicator12, 15.67 | |
| erater1 -> indicator1, lambda_erater1_indicator1, 14.12 | |
| erater1 -> indicator2, lambda_erater1_indicator2, 6.71 | |
| erater1 -> indicator3, lambda_erater1_indicator3, 18.31 | |
| erater1 -> indicator4, lambda_erater1_indicator4, 31.81 | |
| erater1 -> indicator5, lambda_erater1_indicator5, 95.69 | |
| erater1 -> indicator6, lambda_erater1_indicator6, 38.13 | |
| erater2 -> indicator7, lambda_erater2_indicator7, 70.70 | |
| erater2 -> indicator8, lambda_erater2_indicator8, 31.51 | |
| erater2 -> indicator9, lambda_erater2_indicator9, 90.83 | |
| erater2 -> indicator10, lambda_erater2_indicator10, 12.99 | |
| erater2 -> indicator11, lambda_erater2_indicator11, 53.06 | |
| erater2 -> indicator12, lambda_erater2_indicator12, 52.19 | |
| edemoc <-> edemoc, NA, 33.33 | |
| erater1 <-> erater1, NA, 25 | |
| erater2 <-> erater2, NA, 225 | |
| edemoc <-> erater1, NA, 0 | |
| edemoc <-> erater2, NA, 0 | |
| erater1 <-> erater2, NA, 0 | |
| indicator1 <-> indicator1, NA, 673531.2803 | |
| indicator2 <-> indicator2, NA, 17596739.13 | |
| indicator3 <-> indicator3, NA, 46940.98728 | |
| indicator4 <-> indicator4, NA, 10422468.383 | |
| indicator5 <-> indicator5, NA, 3192325.784 | |
| indicator6 <-> indicator6, NA, 700590.022 | |
| indicator7 <-> indicator7, NA, 1976572.886 | |
| indicator8 <-> indicator8, NA, 9677149.536 | |
| indicator9 <-> indicator9, NA, 1305505.098 | |
| indicator10 <-> indicator10, NA, 13204.38979 | |
| indicator11 <-> indicator11, NA, 581054.330 | |
| indicator12 <-> indicator12, NA, 14681009.32 | |
| ### create subroutines | |
| sub1 <- function(n) { # create empty objects to store estimates | |
| coefs1 <<- vector(length=n) | |
| sds1 <<- vector(length=n) | |
| ts1 <<- vector(length=n) | |
| ps1 <<- vector(length=n) | |
| coefs2 <<- vector(length=n) | |
| sds2 <<- vector(length=n) | |
| ts2 <<- vector(length=n) | |
| ps2 <<- vector(length=n) | |
| } | |
| sub2 <- function() { # generate simulated factors | |
| democ <<- runif(n=186, min=0, max=20) | |
| rater1 <<- rnorm(n=186, mean=5, sd=5) | |
| rater2 <<- rnorm(n=186, mean=5, sd=15) | |
| factors <<- cbind(democ, rater1, rater2) | |
| fulldata <<- cbind(bolpaxdata, factors) | |
| } | |
| sub3 <- function() { # generate simulated errors | |
| error1 <<- rnorm(n=186, mean=0, sd=827) + rbeta(n=186, shape1=0.68, shape2=0.78) | |
| error2 <<- rnorm(n=186, mean=0, sd=4188) + rbeta(n=186, shape1=0.10, shape2=0.72) | |
| error3 <<- rnorm(n=186, mean=0, sd=228) + rbeta(n=186, shape1=0.58, shape2=0.67) | |
| error4 <<- rnorm(n=186, mean=0, sd=3237) + rbeta(n=186, shape1=0.50, shape2=0.60) | |
| error5 <<- rnorm(n=186, mean=0, sd=1965) + rbeta(n=186, shape1=0.06, shape2=0.83) | |
| error6 <<- rnorm(n=186, mean=0, sd=734) + rbeta(n=186, shape1=0.15, shape2=0.86) | |
| error7 <<- rnorm(n=186, mean=0, sd=1439) + rbeta(n=186, shape1=0.51, shape2=0.46) | |
| error8 <<- rnorm(n=186, mean=0, sd=2983) + rbeta(n=186, shape1=0.23, shape2=0.40) | |
| error9 <<- rnorm(n=186, mean=0, sd=1190) + rbeta(n=186, shape1=0.73, shape2=0.21) | |
| error10 <<- rnorm(n=186, mean=0, sd=112) + rbeta(n=186, shape1=0.26, shape2=0.63) | |
| error11 <<- rnorm(n=186, mean=0, sd=806) + rbeta(n=186, shape1=0.54, shape2=0.37) | |
| error12 <<- rnorm(n=186, mean=0, sd=4299) + rbeta(n=186, shape1=0.13, shape2=0.46) | |
| errors <<- cbind(error1, error2, error3, error4, error5, error6, error7, error8, error9, error10, error11, error12) | |
| fulldata <<- cbind(fulldata, errors) | |
| } | |
| sub4 <- function(prec=1, ...) { # generate simulated indicators | |
| indicator1 <<- (14.12 * fulldata$rater1) + (69.87 * democ) + error1/prec | |
| indicator2 <<- (6.71 * fulldata$rater1) + (68.57 * democ) + error2/prec | |
| indicator3 <<- (18.31 * fulldata$rater1) + (53.45 * democ) + error3/prec | |
| indicator4 <<- (31.81 * fulldata$rater1) + (28.21 * democ) + error4/prec | |
| indicator5 <<- (95.69 * fulldata$rater1) + (40.63 * democ) + error5/prec | |
| indicator6 <<- (38.13 * fulldata$rater1) + (97.69 * democ) + error6/prec | |
| indicator7 <<- (70.70 * fulldata$rater2) + (21.17 * democ) + error7/prec | |
| indicator8 <<- (31.51 * fulldata$rater2) + (51.63 * democ) + error8/prec | |
| indicator9 <<- (90.83 * fulldata$rater2) + (26.09 * democ) + error9/prec | |
| indicator10 <<- (12.99 * fulldata$rater2) + (55.01 * democ) + error10/prec | |
| indicator11 <<- (53.06 * fulldata$rater2) + (63.13 * democ) + error11/prec | |
| indicator12 <<- (52.19 * fulldata$rater2) + (15.67 * democ) + error12/prec | |
| indicators <<- cbind(indicator1, indicator2, indicator3, indicator4, indicator5, indicator6, indicator7, indicator8, indicator9, indicator10, indicator11, indicator12) | |
| fulldata <<- cbind(fulldata, indicators) | |
| } | |
| sub5 <- function() { # run CFA model | |
| cfadata <<- fulldata[c(55:66)] | |
| cfadata.cov <<- cov(cfadata) | |
| cfadata.sem <<- sem(model.cfadata, cfadata.cov, nrow(cfadata)) | |
| fulldata <<- cbind(fulldata, fscores(cfadata.sem,data=cfadata)) | |
| } | |
| sub6 <- function() { # regress factor scores on country-level variables | |
| factor1reg <<- lm(fulldata$erater1 ~ fulldata$marxist + fulldata$lenergy + fulldata$protestant + fulldata$catholic + fulldata$lage + fulldata$monarchy + fulldata$coups + fulldata$war + fulldata$lprotests + fulldata$lstrikes + fulldata$lriots + fulldata$lcoverage + fulldata$lpopulation + fulldata$larea + fulldata$lradiostvs) | |
| factor2reg <<- lm(fulldata$erater2 ~ fulldata$marxist + fulldata$lenergy + fulldata$protestant + fulldata$catholic + fulldata$lage + fulldata$monarchy + fulldata$coups + fulldata$war + fulldata$lprotests + fulldata$lstrikes + fulldata$lriots + fulldata$lcoverage + fulldata$lpopulation + fulldata$larea + fulldata$lradiostvs) | |
| } | |
| sub7 <- function() { # collect estimates | |
| coefs1 <<- coefs1 | |
| sds1 <<- sds1 | |
| ts1 <<- ts1 | |
| ps1 <<- ps1 | |
| coefs2 <<- coefs2 | |
| sds2 <<- sds2 | |
| ts2 <<- ts2 | |
| ps2 <<- ps2 | |
| estimates <<- cbind(coefs1, sds1, ts1, ps1, coefs2, sds2, ts2, ps2) | |
| } | |
| ### set bias and precision levels | |
| ## set bias levels | |
| bias1 = c(20, 15, 10, 7, 5, 3, 1, 0.5, 0) | |
| bias2 = append(rep(c(0.025), 8), 0) | |
| bias3 = c(1, 1.3, 1.5, 1.7, 2.3, 2.5, 2.7, 2.9, 3.3) | |
| bias4 = c(1, 1.35, 1.55, 1.75, 2.35, 2.55, 2.75, 2.95, 3.35) | |
| ## set precision levels | |
| precs = c(1, 0.001, 1000) | |
| ##### part 1: marxism | |
| ### define master function | |
| marxfunc <- function(n=1, bias1=0, bias2=0, prec=1, ...) { | |
| sub1(n) # create empty objects to store estimates | |
| for(t in 1:n) { | |
| sub2() # generate simulated factors | |
| # introduce systematic bias (additive) | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$marxist[i] == 1) { | |
| fulldata$rater1[i] <<- fulldata$rater1[i] + bias1 | |
| } | |
| } | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$marxist[i] == 1) { | |
| fulldata$rater2[i] <<- fulldata$rater2[i] + bias2 | |
| } | |
| } | |
| sub3() # generate simulated errors | |
| sub4() # generate simulated indicators | |
| sub5() # run CFA model | |
| sub6() # regress factor scores on country-level variables | |
| # extract estimates | |
| coefs1[t] <<- summary(factor1reg)$coef[2,1] | |
| sds1[t] <<- summary(factor1reg)$coef[2,2] | |
| ts1[t] <<- summary(factor1reg)$coef[2,3] | |
| ps1[t] <<- summary(factor1reg)$coef[2,4] | |
| coefs2[t] <<- summary(factor2reg)$coef[2,1] | |
| sds2[t] <<- summary(factor2reg)$coef[2,2] | |
| ts2[t] <<- summary(factor2reg)$coef[2,3] | |
| ps2[t] <<- summary(factor2reg)$coef[2,4] | |
| } | |
| sub7() # collect estimates | |
| } | |
| ### run master function | |
| ## create container to store results | |
| fails.marx <- matrix(nrow=9, ncol=3) | |
| rownames(fails.marx) <- c("bias1=20; bias2=0.025", "bias1=15; bias2=0.025", "bias1=10; bias2=0.025", "bias1=7; bias2=0.025", "bias1=5; bias2=0.025", "bias1=3; bias2=0.025", "bias1=1; bias2=0.025", "bias1=.5; bias2=0.025", "bias1=0; bias2=0") | |
| colnames(fails.marx) <- c("prec=1", "prec=0.001", "prec=1000") | |
| ## compute estimates | |
| for(t in 1:9) { | |
| print(paste("Batch", t)) | |
| for(u in 1:3) { | |
| marxfunc(1000, bias1[t], bias2[t], precs[u]) | |
| estimates <- data.frame(estimates) | |
| fails.marx[t,u] <- length(estimates$coefs1[(estimates$coefs1>0 & estimates$coefs2<0) & (estimates$ps1<0.1 & estimates$ps2<0.1)]) | |
| } | |
| } | |
| ##### part 2: protestantism | |
| ### define master function | |
| protfunc <- function(n=1, bias1=1, bias2=1, prec=1, ...) { | |
| sub1(n) # create empty objects to store estimates | |
| for(t in 1:n) { | |
| sub2() # generate simulated factors | |
| # introduce systematic bias (multiplicative) | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$protestant[i] == 1) { | |
| fulldata$rater1[i] <<- fulldata$rater1[i] * bias1 | |
| } | |
| } | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$protestant[i] == 1) { | |
| fulldata$rater2[i] <<- fulldata$rater2[i] * bias2 | |
| } | |
| } | |
| sub3() # generate simulated errors | |
| sub4() # generate simulated indicators | |
| sub5() # run CFA model | |
| sub6() # regress factor scores on country-level variables | |
| # extract estimates | |
| coefs1[t] <<- summary(factor1reg)$coef[4,1] | |
| sds1[t] <<- summary(factor1reg)$coef[4,2] | |
| ts1[t] <<- summary(factor1reg)$coef[4,3] | |
| ps1[t] <<- summary(factor1reg)$coef[4,4] | |
| coefs2[t] <<- summary(factor2reg)$coef[4,1] | |
| sds2[t] <<- summary(factor2reg)$coef[4,2] | |
| ts2[t] <<- summary(factor2reg)$coef[4,3] | |
| ps2[t] <<- summary(factor2reg)$coef[4,4] | |
| } | |
| sub7() # collect estimates | |
| } | |
| ### run master function | |
| ## create container to store results | |
| fails.prot <- matrix(nrow=9, ncol=3) | |
| rownames(fails.prot) <- c("bias1=bias2=1", "bias1=1.3; bias2=1.35", "bias1=1.5; bias2=1.55", "bias1=1.7; bias2=1.75", "bias1=2.3; bias2=2.35", "bias1=2.5; bias2=2.55", "bias1=2.7; bias2=2.75", "bias1=2.9; bias2=2.95", "bias1=3.3; bias2=3.35") | |
| colnames(fails.prot) <- c("prec=1", "prec=0.001", "prec=1000") | |
| ## compute estimates | |
| for(t in 1:9) { | |
| print(paste("Batch", t)) | |
| for(u in 1:3) { | |
| protfunc(1000, bias3[t], bias4[t], precs[u]) | |
| estimates <- data.frame(estimates) | |
| fails.prot[t,u] <- length(estimates$ps1[estimates$ps1>0.1 & estimates$ps2>0.1]) | |
| } | |
| } | |
| ##### part 3: catholicism | |
| ### define master function | |
| cathfunc <- function(n=1, bias1=0, bias2=0, prec=1, ...) { | |
| sub1(n) # create empty objects to store estimates | |
| for(t in 1:n) { | |
| sub2() # generate simulated factors | |
| # introduce systematic bias (additive) | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$catholic[i] == 1) { | |
| fulldata$rater1[i] <<- fulldata$rater1[i] + bias1 | |
| } | |
| } | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$catholic[i] == 1) { | |
| fulldata$rater2[i] <<- fulldata$rater2[i] + bias2 | |
| } | |
| } | |
| sub3() # generate simulated errors | |
| sub4() # generate simulated indicators | |
| sub5() # run CFA model | |
| sub6() # regress factor scores on country-level variables | |
| # extract estimates | |
| coefs1[t] <<- summary(factor1reg)$coef[5,1] | |
| sds1[t] <<- summary(factor1reg)$coef[5,2] | |
| ts1[t] <<- summary(factor1reg)$coef[5,3] | |
| ps1[t] <<- summary(factor1reg)$coef[5,4] | |
| coefs2[t] <<- summary(factor2reg)$coef[5,1] | |
| sds2[t] <<- summary(factor2reg)$coef[5,2] | |
| ts2[t] <<- summary(factor2reg)$coef[5,3] | |
| ps2[t] <<- summary(factor2reg)$coef[5,4] | |
| } | |
| sub7() # collect estimates | |
| } | |
| ### run master function | |
| ## create container to store results | |
| fails.cath <- matrix(nrow=9, ncol=3) | |
| rownames(fails.cath) <- c("bias1=20; bias2=0.025", "bias1=15; bias2=0.025", "bias1=10; bias2=0.025", "bias1=7; bias2=0.025", "bias1=5; bias2=0.025", "bias1=3; bias2=0.025", "bias1=1; bias2=0.025", "bias1=.5; bias2=0.025", "bias1=0; bias2=0") | |
| colnames(fails.cath) <- c("prec=1", "prec=0.001", "prec=1000") | |
| ## compute estimates | |
| for(t in 1:9) { | |
| print(paste("Batch", t)) | |
| for(u in 1:3) { | |
| cathfunc(1000, bias1[t], bias2[t], precs[u]) | |
| estimates <- data.frame(estimates) | |
| fails.cath[t,u] <- length(estimates$coefs1[estimates$coefs1>0 & estimates$ps1<0.1 & estimates$ps2>0.1]) | |
| } | |
| } | |
| ##### part 4: monarchy | |
| ### define master function | |
| monfunc <- function(n=1, bias1=1, bias2=1, prec=1, ...) { | |
| sub1(n) # create empty objects to store estimates | |
| for(t in 1:n) { | |
| sub2() # generate simulated factors | |
| # introduce systematic bias (multiplicative) | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$monarchy[i] == 1) { | |
| fulldata$rater1[i] <<- fulldata$rater1[i] * bias1 | |
| } | |
| } | |
| for(i in 1:nrow(fulldata)) { | |
| if(fulldata$monarchy[i] == 1) { | |
| fulldata$rater2[i] <<- fulldata$rater2[i] * bias2 | |
| } | |
| } | |
| sub3() # generate simulated errors | |
| sub4() # generate simulated indicators | |
| sub5() # run CFA model | |
| sub6() # regress factor scores on country-level variables | |
| # extract estimates | |
| coefs1[t] <<- summary(factor1reg)$coef[7,1] | |
| sds1[t] <<- summary(factor1reg)$coef[7,2] | |
| ts1[t] <<- summary(factor1reg)$coef[7,3] | |
| ps1[t] <<- summary(factor1reg)$coef[7,4] | |
| coefs2[t] <<- summary(factor2reg)$coef[7,1] | |
| sds2[t] <<- summary(factor2reg)$coef[7,2] | |
| ts2[t] <<- summary(factor2reg)$coef[7,3] | |
| ps2[t] <<- summary(factor2reg)$coef[7,4] | |
| } | |
| sub7() # collect estimates | |
| } | |
| ### run master function | |
| ## create container to store results | |
| fails.mon <- matrix(nrow=9, ncol=3) | |
| rownames(fails.mon) <- c("bias1=bias2=1", "bias1=1.3; bias2=1.35", "bias1=1.5; bias2=1.55", "bias1=1.7; bias2=1.75", "bias1=2.3; bias2=2.35", "bias1=2.5; bias2=2.55", "bias1=2.7; bias2=2.75", "bias1=2.9; bias2=2.95", "bias1=3.3; bias2=3.35") | |
| colnames(fails.mon) <- c("prec=1", "prec=0.001", "prec=1000") | |
| ## compute estimates | |
| for(t in 1:9) { | |
| print(paste("Batch", t)) | |
| for(u in 1:3) { | |
| monfunc(1000, bias3[t], bias4[t], precs[u]) | |
| estimates <- data.frame(estimates) | |
| fails.mon[t,u] <- length(estimates$ps1[estimates$ps1>0.1 & estimates$ps2>0.1]) | |
| } | |
| } | |
| ##### part 5: show all results | |
| fails.marx | |
| fails.prot | |
| fails.cath | |
| fails.mon |
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