difNLR (version 1.3.7)

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

data.frame or matrix: dataset which rows represent unscored examinee answers (nominal) and columns correspond to the items.

group

numeric: binary vector of group membership. "0" for reference group, "1" for focal group.

key

character: the answer key. Each element corresponds to the correct answer of one item.

type

character: type of DDF to be tested. Either "both" for uniform and non-uniform DDF (i.e., difference in parameters "a" and "b") (default), or "udif" for uniform DDF only (i.e., difference in difficulty parameter "b"), or "nudif" for non-uniform DDF only (i.e., difference in discrimination parameter "a"). Can be specified as a single value (for all items) or as an item-specific vector.

match

numeric or character: matching criterion to be used as an estimate of trait. Can be either "zscore" (default, standardized total score), "score" (total test score), or vector of the same length as number of observations in Data.

anchor

character or numeric: specification of DIF free items. A vector of item identifiers (integers specifying the column number) specifying which items are currently considered as anchor (DIF free) items. Argument is ignored if match is not "zscore" or "score".

p.adjust.method

character: method for multiple comparison correction. Possible values are "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", and "none" (default). For more details see p.adjust.

parametrization

character: parametrization of regression coefficients. Possible options are "irt" for difficulty-discrimination parametrization (default) and "classic" for intercept-slope parametrization. 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. Probability of selection the \(k\)-th category (distractor) is $$P(y = k) = exp((a_k + a_kDif*g)*(x - b_k - b_kDif*g)))/(1 + \sum exp((a_l + a_lDif*g)*(x - b_l - b_lDif*g))), $$ where \(x\) is by default standardized total score (also called Z-score) and \(g\) is a group membership. Parameters \(a_k\) and \(b_k\) are discrimination and difficulty for the \(k\)-th category. Terms \(a_kDif\) and \(b_kDif\) then represent differences between two groups (reference and focal) in relevant parameters. Probability of correct answer (specified in argument key) is $$P(y = k) = 1/(1 + \sum exp((a_l + a_lDif*g)*(x - b_l - b_lDif*g))). $$ Parameters are estimated via neural networks. For more details see multinom.

Argument parametrization is a character which specifies parametrization of regression parameters. Default option is "irt" which returns IRT parametrization (difficulty-discrimination, see above). Option "classic" returns intercept-slope parametrization with effect of group membership and interaction with matching criterion, i.e. \(b_0k + b_1k*x + b_2k*g + b_3k*x*g\) instead of \((a_k + a_kDif*g)*(x - b_k - b_kDif*g))\).

References

Agresti, A. (2010). Analysis of ordinal categorical data. Second edition. John Wiley & Sons.

Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection. The R journal, 12(1), 300--323, 10.32614/RJ-2020-014.

See Also

p.adjust multinom

Examples

# 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 {
# }