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=c(scale,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

IPchem$IPchem04_rc[IPchem$IPchem04 == 1] <- 4
IPchem$IPchem04_rc[IPchem$IPchem04 == 2] <- 3
IPchem$IPchem04_rc[IPchem$IPchem04 == 3] <- 2
IPchem$IPchem04_rc[IPchem$IPchem04 == 4] <- 1
IPchem$IPchem04 <- IPchem$IPchem04_rc
IPchem <- subset(IPchem, select=-c(IPchem04_rc))

Instructor Growth Mindset

Items

  1. Instructors in chemistry believe that most students are capable of meeting the course expectations.
  2. Instructors in chemistry believe that most students are capable of getting an ‘A’ if they put in the effort.
  3. Instructors in chemistry see this course as a “weed out” course to fail weaker students.
  4. The instructor expects the course to take a lot of effort.

Stats - Original

Univariate Stats

d <- subset(IPchem, scale == "orig", select=-c(scale))
IPchem_desc <- data.frame(describe(d))
datatable(subset(IPchem_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)

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=.0, sort=TRUE)
## 
## Call:
## factanal(x = d, factors = 1, rotation = "promax", cutoff = 0.3)
## 
## Uniquenesses:
## IPchem02 IPchem03 IPchem04 IPchem05 
##    0.723    0.005    0.927    0.984 
## 
## Loadings:
## [1]  0.526  0.997  0.270 -0.127
## 
##                Factor1
## SS loadings      1.361
## Proportion Var   0.340
## 
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 18.07 on 2 degrees of freedom.
## The p-value is 0.000119

Stats - Alternative

Univariate Stats

d <- subset(IPchem, scale == "alt", select=-c(scale))
IPchem_desc <- data.frame(describe(d))
datatable(subset(IPchem_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 6 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=.0, sort=TRUE)
## 
## Call:
## factanal(x = d, factors = 1, rotation = "promax", cutoff = 0.3)
## 
## Uniquenesses:
## IPchem02 IPchem03 IPchem04 IPchem05 
##    0.547    0.339    0.798    0.992 
## 
## Loadings:
## [1]  0.673  0.813  0.449 -0.091
## 
##                Factor1
## SS loadings      1.324
## Proportion Var   0.331
## 
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 3.3 on 2 degrees of freedom.
## The p-value is 0.192

2PL Model - Orig (1F)

Summary & Fit

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

d1 <- subset(d, select=c(IPchem02, IPchem03, IPchem04))

d <- d1

mod2 <- ltm(d ~ z1)
summary(mod2)
## 
## Call:
## ltm(formula = d ~ z1)
## 
## Model Summary:
##   log.Lik    AIC      BIC
##  -147.925 307.85 322.2167
## 
## Coefficients:
##                   value std.err  z.vals
## Dffclt.IPchem02 -0.9600  0.3990 -2.4063
## Dffclt.IPchem03  0.1031  0.2003  0.5147
## Dffclt.IPchem04  0.6146  0.3145  1.9540
## Dscrmn.IPchem02  1.5563  1.0299  1.5111
## Dscrmn.IPchem03  1.7081  1.0979  1.5557
## Dscrmn.IPchem04  1.2192  0.6155  1.9809
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 0.0042 
## quasi-Newton: BFGS
item.fit(mod2, simulate.p.value=T)
## 
## Item-Fit Statistics and P-values
## 
## Call:
## ltm(formula = d ~ z1)
## 
## Alternative: Items do not fit the model
## Ability Categories: 10
## Monte Carlo samples: 100 
## 
##              X^2 Pr(>X^2)
## IPchem02 44.4591   0.5941
## IPchem03 42.7976   0.5347
## IPchem04 59.2391   0.4257

ICC

plot.ltm(mod2, type = 'ICC', auto.key = FALSE)

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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“auto.key” is not a graphical parameter

IIC

plot.ltm(mod2, type = 'IIC', auto.key = FALSE)

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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“auto.key” is not a graphical parameter

Individual ICC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot.ltm(mod2, 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

Individual IIC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot.ltm(mod2, type = 'IIC', 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(mod2, type=c("IIC"), items=c(0), ylim=c(0,2.1))

2PL Model - Alt (1F)

Summary & Fit

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

d1 <- subset(d, select=c(IPchem02, IPchem03, IPchem04))

d <- d1

mod2 <- ltm(d ~ z1)
summary(mod2)
## 
## Call:
## ltm(formula = d ~ z1)
## 
## Model Summary:
##    log.Lik     AIC      BIC
##  -174.5745 361.149 376.8988
## 
## Coefficients:
##                   value std.err  z.vals
## Dffclt.IPchem02 -1.1948  0.3389 -3.5256
## Dffclt.IPchem03 -0.1744  0.1612 -1.0824
## Dffclt.IPchem04  0.1648  0.2057  0.8014
## Dscrmn.IPchem02  1.9135  1.0015  1.9106
## Dscrmn.IPchem03  2.2822  1.4038  1.6257
## Dscrmn.IPchem04  1.3364  0.5566  2.4013
## 
## Integration:
## method: Gauss-Hermite
## quadrature points: 21 
## 
## Optimization:
## Convergence: 0 
## max(|grad|): 0.0012 
## quasi-Newton: BFGS
item.fit(mod2, simulate.p.value=T)
## 
## Item-Fit Statistics and P-values
## 
## Call:
## ltm(formula = d ~ z1)
## 
## Alternative: Items do not fit the model
## Ability Categories: 10
## Monte Carlo samples: 100 
## 
##              X^2 Pr(>X^2)
## IPchem02 49.0220   0.5347
## IPchem03 39.2038   0.5842
## IPchem04 70.5562   0.5446

ICC

plot.ltm(mod2, type = 'ICC', auto.key = FALSE)

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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“auto.key” is not a graphical parameter

IIC

plot.ltm(mod2, type = 'IIC', auto.key = FALSE)

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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“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 text.default(z[pos[it]], pr[pos[it], itms[it]], labels = nams[it], :

“auto.key” is not a graphical parameter

Individual ICC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot.ltm(mod2, 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

Individual IIC Plots

items <- colnames(d)
n <- 1
for (i in 1:ncol(d)) {
  plot.ltm(mod2, type = 'IIC', 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(mod2, type=c("IIC"), items=c(0), ylim=c(0,2.1))