rm(list=ls()); gc(full=T); objects()
set.seed(10012)gmo$polknowTF<-(gmo$pk_medmarij+gmo$pk_nafta+gmo$pk_parisagree+
gmo$pk_guantanamo+gmo$pk_gdpgrow+gmo$pk_deficit2018)
table(gmo$polknowTF)
gmo$polknowMC<-(gmo$pkT_medmarij+gmo$pkF_nafta+gmo$pkT_parisagree+
gmo$pkF_guantanamo+gmo$pkT_gdpgrow+gmo$pkF_deficit2018)
table(gmo$polknowMC)polMC<-subset(gmo, select=c(pk_medmarij, pk_nafta, pk_parisagree,
pk_guantanamo, pk_deficit2018, pk_gdpgrow,
polknowMC))
psych::describe(polMC); polMC<-na.omit(polMC) # Remover NAs
polTF<-subset(gmo, select=c(pkT_medmarij, pkF_nafta, pkT_parisagree,
pkF_guantanamo, pkF_deficit2018, pkT_gdpgrow, polknowTF))
psych::describe(polTF); polTF<-na.omit(polTF) # Remover NAspol.corMC <- cor(polMC, use="complete.obs")
pol.corMC
pol.corTF <- cor(polTF, use="complete.obs")
pol.corTFLet’s obtain some basic descriptive information about the items. All this information is given by the psychometric package.
psychometric::item.exam(polMC[,1:6], discrim=TRUE, y=polMC[,7])
psychometric::item.exam(polTF[,1:6], discrim=TRUE, y=polTF[,7])
psychometric::alpha(polMC)
psychometric::alpha(polTF)
# Item.total: correlation between items and the total score.
# Item.Tot.woi: correlation between items and the total score by omitting the item.
# Difficulty: proportion of correct responses.
# Discrimination: values above 0.40 are satisfactory and values below 0.19 suggest removal.
?psychometric::item.exam # For each column value
polMC<-subset(gmo, select=c(pk_medmarij, pk_nafta, pk_parisagree,
pk_guantanamo, pk_deficit2018, pk_gdpgrow))
psych::describe(polMC); polMC<-na.omit(polMC)
polTF<-subset(gmo, select=c(pkT_medmarij, pkF_nafta, pkT_parisagree,
pkF_guantanamo, pkF_deficit2018, pkT_gdpgrow))
psych::describe(polTF); polTF<-na.omit(polTF)“ltm” package
# Discrimination fixed at 1 (not allowed to vary)
fitMC <- ltm::rasch(polMC, constraint=cbind(ncol(polMC) +1, 1)) # N of cols, +1, 1 (fixed)
summary(fitMC) # 'value' column is each item difficulty + std.err
# Model Summary: logLik, AIC, and BIC are model fit stats
# Rasch for binary variables (0 or 1)
fitTF <- ltm::rasch(polTF_01, constraint=cbind(length(polTF_01) +1, 1)) # N of cols + 1, 1 (fixed)
summary(fitTF) # 'value' column is each item difficulty + std.err
# ICC plot
# # --------------------------------------------------------------------------------------
# the slope parameter is missing, which implies that all slopes are the same.
plot(fitMC, type=c("ICC"))
plot(fitTF, type=c("ICC"))
# they are parallel because model estimation forced them to be
# lowest to highest difficulty coefs
coef(fitMC, prob=TRUE, order=TRUE)
coef(fitTF, prob=TRUE, order=TRUE)
# Test of absolute fit: we want to fail to reject the null.
# # --------------------------------------------------------------------------------------
# Null: the model fits the data (chi-square test)
ltm::GoF.rasch(fitMC, B=1000)
ltm::GoF.rasch(fitTF, B=1000)
ltm::item.fit(fitMC, simulate.p.value = T)
ltm::item.fit(fitTF, simulate.p.value = T)
# Latent trait estimates for Rasch: theta scores for each individual in the sample.
# # --------------------------------------------------------------------------------------
theta.raschMC<-ltm::factor.scores(fitMC)
plot(theta.raschMC)
summary(theta.raschMC$score.dat$z1)
sqrt(var(theta.raschMC$score.dat$z1))
theta.raschTF<-ltm::factor.scores(fitTF)
plot(theta.raschTF)
summary(theta.raschTF$score.dat$z1)
sqrt(var(theta.raschTF$score.dat$z1))fit1MC <- ltm::rasch(polMC)
summary(fit1MC)
plot(fitMC, type=c("ICC")) fit2MC <- ltm::ltm(polMC ~ z1)
summary(fit2MC) # it provides item difficulty and item discrimination
coef(fit2MC, order = TRUE)
# these results show that some items have really different discrimination parameters,
# which affects item difficulties.
fit2TF <- ltm::ltm(polTF ~ z1)
summary(fit2TF) # it provides item difficulty and item discrimination
coef(fit2TF, order = TRUE)
# Plot Item Characteristic Curves for two-parameter model
# # --------------------------------------------------------------------------------------
par(mfrow=c(2,1)); plot(fit2MC, type=c("ICC")); plot(fit2TF, type=c("ICC"))
# Compare with the Rasch Model above...
par(mfrow=c(2,1)); plot(fitMC, type=c("ICC")); plot(fit2MC, type=c("ICC"))
par(mfrow=c(2,1)); plot(fitTF, type=c("ICC")); plot(fit2TF, type=c("ICC"))
# Plot Item Characteristic Curves
plot(fit2MC, type=c("ICC"), items=c(1,6)) # bad items (prob better to exclude)
plot(fit2MC, type=c("ICC"), items=c(2,3,4,5)) # good items
plot(fit2TF, type=c("ICC"), items=c(1,6)) # bad items (prob better to exclude)
plot(fit2TF, type=c("ICC"), items=c(2,3,4,5)) # good items
# Plot Item Information curves (IIC)
# # --------------------------------------------------------------------------------------
# For each item it gives the relative amount of info that the item yields,
# the highest are the most informative, if the slope is shallow, it does not help at all,
# because they do not detect any differences.
par(mfrow=c(2,1))
plot(fit2MC, type=c("IIC"), items=c(1,6))
plot(fit2TF, type=c("IIC"), items=c(1,6))
plot(fit2MC, type=c("IIC"), items=c(2,3,4,5))
plot(fit2TF, type=c("IIC"), items=c(2,3,4,5))
# Overall, we want a curve that stays high among a substantive range of THETA (x-axis)
plot(fit2MC, type=c("IIC"), items=0)
plot(fit2TF, type=c("IIC"), items=0) # The 3-parameter model is usually employed to handle the phenomenon of
# non-random guessing in the case of difficult items.
fit3MC <- ltm::tpm(polMC, type=c("latent.trait"), max.guessing=.25)
fit3MC
plot(fit3MC, type=c("ICC"))
fit3TF <- ltm::tpm(polTF, type=c("latent.trait"), max.guessing=.25)
fit3TF
plot(fit3TF, type=c("ICC"))
par(mfrow=c(2,1))
plot(fit3MC, type=c("IIC"))
plot(fit3TF, type=c("IIC"))
# Warning: The 3-parameter model is known to have numerical problems like non-convergence,
# especially for the guessing parameters. These problems usually result in a zero estimate
# for some guessing parameters and/or in a non positive definite Hessian matrix.
### For mathematical details: https://www.jstatsoft.org/article/view/v017i05