fitted {ltm}

Fitted Values for IRT model

Description

Computes the expected frequencies for vectors of response patterns.

Usage

## S3 method for class 'gpcm'
fitted(object, resp.patterns = NULL, 
    type = c("expected", "marginal-probabilities",
    "conditional-probabilities"), ...)

## S3 method for class 'grm'
fitted(object, resp.patterns = NULL, 
    type = c("expected", "marginal-probabilities",
    "conditional-probabilities"), ...)

## S3 method for class 'ltm'
fitted(object, resp.patterns = NULL, 
    type = c("expected", "marginal-probabilities", 
    "conditional-probabilities"), ...)

## S3 method for class 'rasch'
fitted(object, resp.patterns = NULL, 
    type = c("expected", "marginal-probabilities", 
    "conditional-probabilities"), ...)

## S3 method for class 'tpm'
fitted(object, resp.patterns = NULL, 
    type = c("expected", "marginal-probabilities", 
    "conditional-probabilities"), ...)

Arguments

object

an object inheriting either from class gpcm, class grm, class ltm, class rasch, or class tpm.

resp.patterns

a matrix or a data.frame of response patterns with columns denoting the items; if NULL the expected frequencies are computed for the observed response patterns.

type

if type == "marginal-probabilities" the marginal probabilities for each response are computed; these are given by \int \{ \prod_{i = 1}^p Pr(x_i = 1 | z)^{x_i} \times (1 - Pr(x_i = 1 | z))^{1 - x_i} \}p(z) dz, where x_i denotes the ith item and z the latent variable. If type == "expected" the expected frequencies for each response are computed, which are the marginal probabilities times the number of sample units. If type == "conditional-probabilities" the conditional probabilities for each response and item are computed; these are Pr(x_i = 1 | \hat{z}), where \hat{z} is the ability estimate .

...

additional arguments; currently none is used.

Value

a numeric matrix or a list containing either the response patterns of interest with their expected frequencies or marginal probabilities, if type == "expected" || "marginal-probabilities" or the conditional probabilities for each response pattern and item, if type == "conditional-probabilities".

Author(s)

Dimitris Rizopoulos [e-mail]

See Also

residuals.gpcm, residuals.grm, residuals.ltm, residuals.rasch, residuals.tpm

Examples

fit <- grm(Science[c(1,3,4,7)])
fitted(fit, resp.patterns = matrix(1:4, nr = 4, nc = 4))

fit <- rasch(LSAT)
fitted(fit, type = "conditional-probabilities")