MLR: DDF likelihood ratio statistics based on multinomial log-linear regression model.

Description

Calculates DDF likelihood ratio statistics for nominal data based on multinomial log-linear model.

Usage

MLR(Data, group, key, type = "both", match = "zscore", anchor = 1:ncol(Data),
p.adjust.method = "none", parametrization = "irt", alpha = 0.05)

Arguments

Data

character: the unscored data matrix.

group

numeric or character: the binary vector of group membership

key

character: the answer key.

type

character: type of DDF to be tested (either "both" (default), "udif", or "nudif"). See Details.

match

specifies matching criterion. Can be either "zscore" (default, standardized total score), "score" (total test score), or vector of the same length as number of observations in Data. See Details.

anchor

a vector of integers specifying which items are currently considered as anchor (DDF free) items. By default, all items are considered as anchors. Argument is ignored if match is not "zscore" or "score". See Details.

p.adjust.method

character: method for multiple comparison correction. See Details.

parametrization

character: parametrization of regression coefficients. Possible options are "irt" (default) and "classic". See Details.

alpha

numeric: significance level (default is 0.05).

Value

A list with the following arguments:

Sval: the values of likelihood ratio test statistics.
pval: the p-values by likelihood ratio test.
adj.pval: the adjusted p-values by likelihood ratio test using p.adjust.method.
df: the degress of freedom of likelihood ratio test.
par.m0: the estimates of null model.
par.m1: the estimates of alternative model.
se.m0: standard errors of parameters in null model.
se.m1: standard errors of parameters in alternative model.
ll.m0: log-likelihood of m0 model.
ll.m1: log-likelihood of m1 model.
AIC.m0: AIC of m0 model.
AIC.m1: AIC of m1 model.
BIC.m0: BIC of m0 model.
BIC.m1: BIC of m1 model.

Details

Calculates DDF likelihood ratio statistics based on multinomial log-linear model.

The Data is a matrix which rows represents examinee unscored answers and columns correspond to the items. The group must be a vector of the same length as nrow(Data). The key must be a vector of correct answers corresponding to columns of Data.

The type corresponds to type of DDF to be tested. Possible values are "both" to detect any DDF (uniform and/or non-uniform), "udif" to detect only uniform DDF or "nudif" to detect only non-uniform DDF.

Argument match represents the matching criterion. It can be either the standardized test score (default, "zscore"), total test score ("score"), or any other continuous or discrete variable of the same length as number of observations in Data. Matching criterion is used in NLR function as a covariate in non-linear regression model.

The p.adjust.method is a character for p.adjust function from the stats package. Possible values are "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none". See also p.adjust for more information.

Argument parametrization is a character which specifies parametrization of regression parameters. Default option is "irt" which returns IRT parametrization (difficulty-discrimination). Option "classic" returns intercept-slope parametrization with effect of group membership and interaction with matching criterion.

Examples

Run this code

# NOT RUN {
# loading data based on GMAT
data(GMATtest, GMATkey)

Data  <- GMATtest[, 1:20]
group <- GMATtest[, "group"]
key <- GMATkey

# Testing both DDF effects
MLR(Data, group, key, type = "both")

# Testing uniform DDF effects
MLR(Data, group, key, type = "udif")

# Testing non-uniform DDF effects
MLR(Data, group, key, type = "nudif")
# }
# NOT RUN {
# }