R help - Mar 2008 - ltm package question

Hello All,

I was wondering how I can get the overall Pearson chi^2 test of model fit
with its df and p value in the LTM package for the 2PL models.

Thanks,

-- 
Davood Tofighi
Department of Psychology
Arizona State University

	[[alternative HTML version deleted]]

the Pearson chi^2 is not directly computed in 'ltm', and the reason is 
that both the Pearson chi^2 and the likelihood-ratio statistics do not 
follow the claimed chi-squared distribution, especially as the number 
of items increases. If you still need to compute it, then you can use 
the following simple function:

chisq.irt <- function (object) {
    if (!class(object) %in% c("ltm", "rasch",
"tpm"))
        stop("Use only with 'ltm', 'rasch' or 'tpm'
objects.\n")
    nam.obj <- deparse(substitute(object))
    p <- ncol(object$X)
    X <- expand.grid(rep(list(c(0, 1)), p))
    res <- residuals(object, resp.patterns = data.matrix(X))
    Tstat <- sum((res[, "Resid"])^2)
    df <- 2^p - attr(logLik(object), "df") - 1
    pval <- pchisq(Tstat, df, lower.tail = FALSE)
    names(Tstat) <- "X^2"
    names(df) <- "df"
    rval <- list(statistic = Tstat, parameter = df, p.value = pval,
        alternative = "the fitted IRT model is not appropriate for the 
data set",
        method = "Pearson X^2 for IRT Models",
        data.name = paste("data from model '", nam.obj,
"'", sep =
""))
    class(rval) <- "htest"
    rval
}

# Some examples
library(ltm)
fitRasch <- rasch(LSAT, constraint = cbind(length(LSAT) + 1, 1))
fit1PL <- rasch(LSAT)
fit2PL <- ltm(LSAT ~ z1)

chisq.irt(fitRasch)
chisq.irt(fit1PL)
chisq.irt(fit2PL)

# check also which perform a Bootstrap approximation
# to the distribution of the statistic uner the null
GoF.rasch(fitRasch)
GoF.rasch(fit1PL)


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Davood Tofighi" <dtofighi at asu.edu>
To: <r-help at r-project.org>
Sent: Monday, March 10, 2008 4:16 AM
Subject: [R] ltm package question

> Hello All,
>
> I was wondering how I can get the overall Pearson chi^2 test of 
> model fit
> with its df and p value in the LTM package for the 2PL models.
>
> Thanks,
>
> -- 
> Davood Tofighi
> Department of Psychology
> Arizona State University
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
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> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

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