| LSAT6 {mirt} | R Documentation |
Data from Thissen (1982); contains 5 dichotomously scored items obtained from the Law School Admissions Test, section 6.
Phil Chalmers rphilip.chalmers@gmail.com
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 175-186.
## No test:
dat <- expand.table(LSAT6)
head(dat)
## Item_1 Item_2 Item_3 Item_4 Item_5
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 0 0 0 0 1
## 5 0 0 0 0 1
## 6 0 0 0 0 1
itemstats(dat)
## $overall
## N mean_total.score sd_total.score ave.r sd.r alpha
## 1000 3.819 1.035 0.077 0.03 0.295
##
## $itemstats
## N mean sd total.r total.r_if_rm alpha_if_rm
## Item_1 1000 0.924 0.265 0.362 0.113 0.275
## Item_2 1000 0.709 0.454 0.567 0.153 0.238
## Item_3 1000 0.553 0.497 0.618 0.173 0.217
## Item_4 1000 0.763 0.425 0.534 0.144 0.246
## Item_5 1000 0.870 0.336 0.435 0.122 0.266
##
## $proportions
## 0 1
## Item_1 0.076 0.924
## Item_2 0.291 0.709
## Item_3 0.447 0.553
## Item_4 0.237 0.763
## Item_5 0.130 0.870
model <- 'F = 1-5
CONSTRAIN = (1-5, a1)'
(mod <- mirt(dat, model))
##
## Call:
## mirt(data = dat, model = model)
##
## Full-information item factor analysis with 1 factor(s).
## Converged within 1e-04 tolerance after 12 EM iterations.
## mirt version: 1.40
## M-step optimizer: BFGS
## EM acceleration: Ramsay
## Number of rectangular quadrature: 61
## Latent density type: Gaussian
##
## Log-likelihood = -2466.938
## Estimated parameters: 10
## AIC = 4945.875
## BIC = 4975.322; SABIC = 4956.265
## G2 (25) = 21.8, p = 0.6474
## RMSEA = 0, CFI = NaN, TLI = NaN
M2(mod)
## M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI CFI
## stats 5.292566 9 0.8080952 0 0 0.02254275 0.02242068 1.072511 1
itemfit(mod)
## item S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
## 1 Item_1 0.436 2 0 0.804
## 2 Item_2 1.576 2 0 0.455
## 3 Item_3 0.871 1 0 0.351
## 4 Item_4 0.190 2 0 0.909
## 5 Item_5 0.190 2 0 0.909
coef(mod, simplify=TRUE)
## $items
## a1 d g u
## Item_1 0.755 2.730 0 1
## Item_2 0.755 0.999 0 1
## Item_3 0.755 0.240 0 1
## Item_4 0.755 1.307 0 1
## Item_5 0.755 2.100 0 1
##
## $means
## F
## 0
##
## $cov
## F
## F 1
# equivalentely, but with a different parameterization
mod2 <- mirt(dat, 1, itemtype = 'Rasch')
anova(mod, mod2) #equal
## AIC SABIC HQ BIC logLik X2 df p
## mod 4945.875 4956.265 4957.067 4975.322 -2466.938
## mod2 4945.875 4956.266 4957.067 4975.322 -2466.938 0 0 NaN
M2(mod2)
## M2 df p RMSEA RMSEA_5 RMSEA_95 SRMSR TLI CFI
## stats 5.292778 9 0.8080758 0 0 0.02254382 0.02242585 1.072507 1
itemfit(mod2)
## item S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
## 1 Item_1 0.436 2 0 0.804
## 2 Item_2 1.576 2 0 0.455
## 3 Item_3 0.872 1 0 0.351
## 4 Item_4 0.190 2 0 0.909
## 5 Item_5 0.190 2 0 0.909
coef(mod2, simplify=TRUE)
## $items
## a1 d g u
## Item_1 1 2.731 0 1
## Item_2 1 0.999 0 1
## Item_3 1 0.240 0 1
## Item_4 1 1.307 0 1
## Item_5 1 2.100 0 1
##
## $means
## F1
## 0
##
## $cov
## F1
## F1 0.572
sqrt(coef(mod2)$GroupPars[2]) #latent SD equal to the slope in mod
## [1] 0.7561839
## End(No test)