Data from Bock & Lieberman (1970); contains 5 dichotomously scored items obtained from the Law School Admissions Test, section 7.
Data from
References
Bock, R. D., & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35(2), 179-197.
Bock, R. D., & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35(2), 179-197.
Author
Phil Chalmers rphilip.chalmers@gmail.com
Examples
# \donttest{
dat <- expand.table(LSAT7)
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 0
#> 5 0 0 0 0 0
#> 6 0 0 0 0 0
itemstats(dat)
#> $overall
#> N mean_total.score sd_total.score ave.r sd.r alpha SEM.alpha
#> 1000 3.707 1.199 0.143 0.052 0.453 0.886
#>
#> $itemstats
#> N mean sd total.r total.r_if_rm alpha_if_rm
#> Item.1 1000 0.828 0.378 0.530 0.246 0.396
#> Item.2 1000 0.658 0.475 0.600 0.247 0.394
#> Item.3 1000 0.772 0.420 0.611 0.313 0.345
#> Item.4 1000 0.606 0.489 0.592 0.223 0.415
#> Item.5 1000 0.843 0.364 0.461 0.175 0.438
#>
#> $proportions
#> 0 1
#> Item.1 0.172 0.828
#> Item.2 0.342 0.658
#> Item.3 0.228 0.772
#> Item.4 0.394 0.606
#> Item.5 0.157 0.843
#>
(mod <- mirt(dat, 1))
#>
#> Call:
#> mirt(data = dat, model = 1)
#>
#> Full-information item factor analysis with 1 factor(s).
#> Converged within 1e-04 tolerance after 28 EM iterations.
#> mirt version: 1.43
#> M-step optimizer: BFGS
#> EM acceleration: Ramsay
#> Number of rectangular quadrature: 61
#> Latent density type: Gaussian
#>
#> Log-likelihood = -2658.805
#> Estimated parameters: 10
#> AIC = 5337.61
#> BIC = 5386.688; SABIC = 5354.927
#> G2 (21) = 31.7, p = 0.0628
#> RMSEA = 0.023, CFI = NaN, TLI = NaN
coef(mod)
#> $Item.1
#> a1 d g u
#> par 0.988 1.856 0 1
#>
#> $Item.2
#> a1 d g u
#> par 1.081 0.808 0 1
#>
#> $Item.3
#> a1 d g u
#> par 1.706 1.804 0 1
#>
#> $Item.4
#> a1 d g u
#> par 0.765 0.486 0 1
#>
#> $Item.5
#> a1 d g u
#> par 0.736 1.855 0 1
#>
#> $GroupPars
#> MEAN_1 COV_11
#> par 0 1
#>
# }
# \donttest{
dat <- expand.table(LSAT7)
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 0
#> 5 0 0 0 0 0
#> 6 0 0 0 0 0
itemstats(dat)
#> $overall
#> N mean_total.score sd_total.score ave.r sd.r alpha SEM.alpha
#> 1000 3.707 1.199 0.143 0.052 0.453 0.886
#>
#> $itemstats
#> N mean sd total.r total.r_if_rm alpha_if_rm
#> Item.1 1000 0.828 0.378 0.530 0.246 0.396
#> Item.2 1000 0.658 0.475 0.600 0.247 0.394
#> Item.3 1000 0.772 0.420 0.611 0.313 0.345
#> Item.4 1000 0.606 0.489 0.592 0.223 0.415
#> Item.5 1000 0.843 0.364 0.461 0.175 0.438
#>
#> $proportions
#> 0 1
#> Item.1 0.172 0.828
#> Item.2 0.342 0.658
#> Item.3 0.228 0.772
#> Item.4 0.394 0.606
#> Item.5 0.157 0.843
#>
(mod <- mirt(dat, 1))
#>
#> Call:
#> mirt(data = dat, model = 1)
#>
#> Full-information item factor analysis with 1 factor(s).
#> Converged within 1e-04 tolerance after 28 EM iterations.
#> mirt version: 1.43
#> M-step optimizer: BFGS
#> EM acceleration: Ramsay
#> Number of rectangular quadrature: 61
#> Latent density type: Gaussian
#>
#> Log-likelihood = -2658.805
#> Estimated parameters: 10
#> AIC = 5337.61
#> BIC = 5386.688; SABIC = 5354.927
#> G2 (21) = 31.7, p = 0.0628
#> RMSEA = 0.023, CFI = NaN, TLI = NaN
coef(mod)
#> $Item.1
#> a1 d g u
#> par 0.988 1.856 0 1
#>
#> $Item.2
#> a1 d g u
#> par 1.081 0.808 0 1
#>
#> $Item.3
#> a1 d g u
#> par 1.706 1.804 0 1
#>
#> $Item.4
#> a1 d g u
#> par 0.765 0.486 0 1
#>
#> $Item.5
#> a1 d g u
#> par 0.736 1.855 0 1
#>
#> $GroupPars
#> MEAN_1 COV_11
#> par 0 1
#>
# }