Prepare Data

Import surveys, combine into single data frame, delete identifying information, assign IDs, and separate out by scale for item examination.

# https://hansjoerg.me/2018/04/23/rasch-in-r-tutorial/

knitr::knit_hooks$set(
   error = function(x, options) {
     paste('\n\n<div class="alert alert-danger">',
           gsub('##', '\n', gsub('^##\ Error', '**Error**', x)),
           '</div>', sep = '\n')
   },
   warning = function(x, options) {
     paste('\n\n<div class="alert alert-warning">',
           gsub('##', '\n', gsub('^##\ Warning:', '**Warning**', x)),
           '</div>', sep = '\n')
   },
   message = function(x, options) {
     paste('\n\n<div class="alert alert-info">',
           gsub('##', '\n', x),
           '</div>', sep = '\n')
   }
)

# load libraries ----------------------------------------------------------
library(stringi)
library(psych)
library(DT)
library(naniar)
library(UpSetR)
library(nFactors)
library(lavaan)
library(corrplot)
library(tidyr)

library(ggplot2)
library(dplyr)
library("eRm")
library("ltm")
library("difR")
library("psych")

# load data ---------------------------------------------------------------
# alt <- read.csv(file="UBelong Post-Survey Pitt OChem Spring 2022 Alternative Scales_April 28, 2022_12.34.csv", header=T)
# alt <- alt[-c(1,2),]
# alt$scale <- "alt"
# 
# orig <- read.csv(file="UBelong Post-Survey Pitt OChem Spring 2022 Original Scales_April 28, 2022_12.35.csv", header=T)
# orig <- orig[-c(1,2),]
# orig$scale <- "orig"
# 
# df <- rbind.data.frame(alt, orig)
# df <- subset(df, select = -c(1:19))
# names(df)
# myFun <- function(n) {
#   a <- do.call(paste0, replicate(5, sample(LETTERS, n, TRUE), FALSE))
#   paste0(a, sprintf("%04d", sample(9999, n, TRUE)), sample(LETTERS, n, TRUE))
# }
# df$id <- myFun(nrow(df))
# write.csv(df, file="imported_anonymized.csv", row.names = F)

df <- read.csv(file="imported_anonymized.csv", header=T)

# extract items -----------------------------------------------------------
# new items
EEochem <- subset(df, select=c(scale,grep("EEochem", colnames(df)))) # entry expectations
CCdisc <- subset(df, select=c(scale,grep("CCdisc", colnames(df)))) # classroom climate
IDochem <- cbind.data.frame(subset(df, select=c(scale,grep("IDochem", colnames(df)))), subset(df, select=grep("FASochem", colnames(df)))) # identity
CSochem <- subset(df, select=grep("CSochem", colnames(df))) # career satisfaction

# established scales
MSchem <- subset(df, select=c(scale,grep("MSchem", colnames(df)))) # discipline growth mindset (chemistry)
IPchem <- subset(df, select=grep("IPchem", colnames(df))) # instructor growth mindset (chemistry)
SEchem <- subset(df, select=grep("SEchem", colnames(df))) # disciplinary self-efficacy (chemistry)
MSochem <- subset(df, select=c(scale, grep("MSochem", colnames(df)))) # disciplinary growth mindset (organic chemistry)
IPochem <- subset(df, select=grep("IPochem", colnames(df))) # instructor growth mindset (organic chemistry)
SEochem <- subset(df, select=grep("SEochem", colnames(df))) # disciplinary self-efficacy (organic chemistry)
CNEBochem_class <- cbind.data.frame(subset(subset(df, select=grep("CNEBochem", colnames(df))), select=c(1:3))) # entity norms and beliefs
CNEBochem_self <- cbind.data.frame(subset(subset(df, select=grep("CNEBochem", colnames(df))), select=c(4:6))) # entity norms and beliefs
CNHSochem_others <- cbind.data.frame(subset(subset(df, select=grep("CNHSochem", colnames(df))), select=c(1:3))) # help seeking
CNHSochem_self <- cbind.data.frame(subset(subset(df, select=grep("CNHSochem", colnames(df))), select=c(4:6))) # help seeking
CNSWochem <- subset(df, select=grep("CNSWochem", colnames(df))) # help seeking
FCochem <- subset(df, select=grep("FCochem", colnames(df))) # faculty caring

Classroom Climate

Items

  1. Students in this class were competitive with each other
  2. I didn’t feel comfortable studying with others in this class
  3. Other students in this class treated me disrespectfully (1=never; 2=once; 3=several times; 4=frequently)
  4. I had bad experiences in studying with others for this class (1=never; 2=once; 3=several times; 4=frequently)

Stats - Original

Univariate Stats

d <- subset(CCdisc, scale == "orig", select=-c(scale))
CCchem_desc <- data.frame(describe(d))
datatable(subset(CCchem_desc, select=-c(n, trimmed, mad))) %>%
  formatRound(1:10) %>%
  formatStyle(8:9, color = styleInterval(c(-2, 2), c('red', 'black', 'red')))

Missingness

vis_miss(d)

# gg_miss_upset(EEochem)

Histograms

ggplot(gather(d), aes(value)) + 
  geom_histogram(bins = 4) + 
  facet_wrap(~key)

Warning Removed 4 rows containing non-finite values (stat_bin).

Item Correlations

corr <- corr.test(d, adjust = "holm")

rval <- corr$r
rval[lower.tri(corr$r, diag = T)] <- NA

datatable(rval) %>%
  formatRound(1:ncol(rval)) %>%
  formatStyle(1:ncol(rval), color = styleInterval(c(-.7, .7), c('red', 'black', 'red')))
corrplot(corr$r)

EFA

d <- na.omit(d)
ev <- eigen(cor(d))
ap <- parallel(subject=nrow(d),var=ncol(d),rep=100,cent=.05)
nS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)
plotnScree(nS)

EFA <- factanal(d, factors = 1, rotation = "promax", cutoff = 0.3)
print(EFA, digits=3, cutoff=.4, sort=TRUE)
## 
## Call:
## factanal(x = d, factors = 1, rotation = "promax", cutoff = 0.3)
## 
## Uniquenesses:
## CCdisc01 CCdisc02 CCdisc03 CCdisc04 
##    0.966    0.964    0.586    0.005 
## 
## Loadings:
## [1] 0.643 0.997            
## 
##                Factor1
## SS loadings      1.479
## Proportion Var   0.370
## 
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 2.47 on 2 degrees of freedom.
## The p-value is 0.29

Stats - Alternative

Univariate Stats

d <- subset(CCdisc, scale == "alt", select=-c(scale))
CCchem_desc <- data.frame(describe(d))
datatable(subset(CCchem_desc, select=-c(n, trimmed, mad))) %>%
  formatRound(1:10) %>%
  formatStyle(8:9, color = styleInterval(c(-2, 2), c('red', 'black', 'red')))

Missingness

vis_miss(d)

# gg_miss_upset(EEochem)

Histograms

ggplot(gather(d), aes(value)) + 
  geom_histogram(bins = 4) + 
  facet_wrap(~key)

Warning Removed 11 rows containing non-finite values (stat_bin).

Item Correlations

corr <- corr.test(d, adjust = "holm")

rval <- corr$r
rval[lower.tri(corr$r, diag = T)] <- NA

datatable(rval) %>%
  formatRound(1:ncol(rval)) %>%
  formatStyle(1:ncol(rval), color = styleInterval(c(-.7, .7), c('red', 'black', 'red')))
corrplot(corr$r)

EFA

d <- na.omit(d)
ev <- eigen(cor(d))
ap <- parallel(subject=nrow(d),var=ncol(d),rep=100,cent=.05)
nS <- nScree(x=ev$values, aparallel=ap$eigen$qevpea)
plotnScree(nS)

EFA <- factanal(d, factors = 1, rotation = "promax", cutoff = 0.3)
print(EFA, digits=3, cutoff=.4, sort=TRUE)
## 
## Call:
## factanal(x = d, factors = 1, rotation = "promax", cutoff = 0.3)
## 
## Uniquenesses:
## CCdisc01 CCdisc02 CCdisc03 CCdisc04 
##    0.934    0.005    0.991    0.999 
## 
## Loadings:
## [1]  0.997                     
## 
##                Factor1
## SS loadings      1.071
## Proportion Var   0.268
## 
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 2.96 on 2 degrees of freedom.
## The p-value is 0.228

1PL Model - Orig (All)

Summary & Fit

d <- subset(CCdisc, scale == "orig", select=-c(scale))
d <- d %>%
  mutate_at(vars(1:ncol(d)), recode, `1` = 0, `2` = 0, `3` = 1, `4` = 1)

mod <- rasch(d)
summary(mod)
## 
## Call:
## rasch(data = d)
## 
## Model Summary:
##    log.Lik      AIC      BIC
##  -140.9701 291.9402 303.9124
## 
## Coefficients:
##                   value std.err  z.vals
## Dffclt.CCdisc01 -0.3643  0.2380 -1.5305
## Dffclt.CCdisc02  0.5141  0.2492  2.0632
## Dffclt.CCdisc03  3.0657  0.7399  4.1433
## Dffclt.CCdisc04  2.1464  0.5007  4.2871
## Dscrmn           1.3011  0.3391  3.8365
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 0.0034 
## quasi-Newton: BFGS
item.fit(mod, simulate.p.value=T)

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

## 
## Item-Fit Statistics and P-values
## 
## Call:
## rasch(data = d)
## 
## Alternative: Items do not fit the model
## Ability Categories: 10
## Monte Carlo samples: 100 
## 
##              X^2 Pr(>X^2)
## CCdisc01 18.6093   0.6337
## CCdisc02 18.3660   0.5149
## CCdisc03  9.6024   0.2574
## CCdisc04 21.9748   0.0792

ICC

plot(mod, type="ICC", cex = .7, legend = F, col = 1)

IIC

plot(mod, type="IIC", cex = .7, legend = F, col = 1)

Individual ICC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot(mod, type = 'ICC', auto.key = FALSE, items = n, main = items[n], annot = F)
  n <- n + 1
}

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Test Information Function

plot(mod, type=c("IIC"), items=c(0))

1PL Model - Orig (1F)

Summary & Fit

d1 <- subset(d, select=c(CCdisc01, CCdisc02, CCdisc03))

d <- d1

mod <- rasch(d)
summary(mod)
## 
## Call:
## rasch(data = d)
## 
## Model Summary:
##    log.Lik      AIC      BIC
##  -119.4242 246.8484 256.4262
## 
## Coefficients:
##                   value std.err  z.vals
## Dffclt.CCdisc01 -0.5517  0.4447 -1.2406
## Dffclt.CCdisc02  0.7963  0.5291  1.5049
## Dffclt.CCdisc03  4.8681  2.6768  1.8186
## Dscrmn           0.7141  0.4273  1.6713
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 4e-06 
## quasi-Newton: BFGS
item.fit(mod, simulate.p.value=T)

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

## 
## Item-Fit Statistics and P-values
## 
## Call:
## rasch(data = d)
## 
## Alternative: Items do not fit the model
## Ability Categories: 10
## Monte Carlo samples: 100 
## 
##              X^2 Pr(>X^2)
## CCdisc01 31.0271   0.4455
## CCdisc02 29.7570   0.4257
## CCdisc03 17.3357   0.3366

ICC

plot(mod, type="ICC", cex = .7, legend = F, col = 1)

IIC

plot(mod, type="IIC", cex = .7, legend = F, col = 1)

Individual ICC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot(mod, type = 'ICC', auto.key = FALSE, items = n, main = items[n], annot = F)
  n <- n + 1
}

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Test Information Function

plot(mod, type=c("IIC"), items=c(0))

1PL Model - Alt (All)

Summary & Fit

d <- subset(CCdisc, scale == "alt", select=-c(scale))
d <- d %>%
  mutate_at(vars(1:ncol(d)), recode, `1` = 0, `2` = 0, `3` = 1, `4` = 1)

mod <- rasch(d)

Warning in rasch(d): Hessian matrix at convergence is not positive definite; unstable solution.

summary(mod)

Warning in sqrt(diag(new.covar)): NaNs produced

Warning in sqrt(diag(new.covar)): NaNs produced

Warning in sqrt(diag(new.covar)): NaNs produced

Warning in sqrt(diag(new.covar)): NaNs produced

Warning in sqrt(Var[n.ind + 1, n.ind + 1]): NaNs produced

## 
## Call:
## rasch(data = d)
## 
## Model Summary:
##   log.Lik    AIC      BIC
##  -148.455 306.91 320.0348
## 
## Coefficients:
##                      value std.err z.vals
## Dffclt.CCdisc01  -454.8986     NaN    NaN
## Dffclt.CCdisc02  3690.3401     NaN    NaN
## Dffclt.CCdisc03 17011.3772     NaN    NaN
## Dffclt.CCdisc04 11791.5642     NaN    NaN
## Dscrmn              0.0003     NaN    NaN
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 2e-04 
## quasi-Newton: BFGS
item.fit(mod, simulate.p.value=T)

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

## 
## Item-Fit Statistics and P-values
## 
## Call:
## rasch(data = d)
## 
## Alternative: Items do not fit the model
## Ability Categories: 10
## Monte Carlo samples: 100 
## 
##              X^2 Pr(>X^2)
## CCdisc01 18.7374   0.9307
## CCdisc02 48.9937    0.099
## CCdisc03  0.9899   0.6733
## CCdisc04 29.3406   0.1188

ICC

plot(mod, type="ICC", cex = .7, legend = F, col = 1)

IIC

plot(mod, type="IIC", cex = .7, legend = F, col = 1)

Individual ICC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot(mod, type = 'ICC', auto.key = FALSE, items = n, main = items[n], annot = F)
  n <- n + 1
}

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Test Information Function

plot(mod, type=c("IIC"), items=c(0))

1PL Model - Alt (1F)

Summary & Fit

d1 <- subset(d, select=c(CCdisc01, CCdisc03, CCdisc04))

d <- d1

mod <- rasch(d)

Warning in rasch(d): Hessian matrix at convergence is not positive definite; unstable solution.

summary(mod)

Warning in sqrt(diag(new.covar)): NaNs produced

Warning in sqrt(diag(new.covar)): NaNs produced

Warning in sqrt(Var[n.ind + 1, n.ind + 1]): NaNs produced

## 
## Call:
## rasch(data = d)
## 
## Model Summary:
##    log.Lik      AIC      BIC
##  -92.10244 192.2049 202.7048
## 
## Coefficients:
##                   value std.err z.vals
## Dffclt.CCdisc01 -0.1353  0.1952 -0.693
## Dffclt.CCdisc03  4.2319     NaN    NaN
## Dffclt.CCdisc04  2.9291     NaN    NaN
## Dscrmn           1.3738     NaN    NaN
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 2.4 
## quasi-Newton: BFGS
item.fit(mod, simulate.p.value=T)

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

Warning in rasch(data = X.new): Hessian matrix at convergence is not positive definite; unstable solution.

## 
## Item-Fit Statistics and P-values
## 
## Call:
## rasch(data = d)
## 
## Alternative: Items do not fit the model
## Ability Categories: 10
## Monte Carlo samples: 100 
## 
##              X^2 Pr(>X^2)
## CCdisc01 42.9025    0.495
## CCdisc03  2.1319    0.396
## CCdisc04 17.8159   0.5149

ICC

plot(mod, type="ICC", cex = .7, legend = F, col = 1)

IIC

plot(mod, type="IIC", cex = .7, legend = F, col = 1)

Individual ICC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot(mod, type = 'ICC', auto.key = FALSE, items = n, main = items[n], annot = F)
  n <- n + 1
}

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Warning in plot.window(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy, type, …): “auto.key” is not a graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in axis(side = side, at = at, labels = labels, …): “auto.key” is not a

graphical parameter

Warning in box(…): “auto.key” is not a graphical parameter

Warning in title(…): “auto.key” is not a graphical parameter

Warning in plot.xy(xy.coords(x, y), type = type, …): “auto.key” is not a

graphical parameter

Test Information Function

plot(mod, type=c("IIC"), items=c(0))