difORD: DIF detection among ordinal data.
In difNLR: DIF and DDF Detection by Non-Linear Regression Models

difORD

R Documentation

DIF detection among ordinal data.

Description

Performs DIF detection procedure for ordinal data based either on adjacent category logit model or on cumulative logit model and likelihood ratio test of a submodel.

Usage

difORD(Data, group, focal.name, model = "adjacent", type = "both", match = "zscore",
       anchor = NULL, purify = FALSE, nrIter = 10, p.adjust.method = "none",
       alpha = 0.05, parametrization)

Arguments

`Data`	data.frame or matrix: dataset which rows represent ordinaly scored examinee answers and columns correspond to the items. In addition, `Data` can hold the vector of group membership.
`group`	numeric or character: a dichotomous vector of the same length as `nrow(Data)` or a column identifier of `Data`.
`focal.name`	numeric or character: indicates the level of `group` which corresponds to focal group.
`model`	character: logistic regression model for ordinal data (either `"adjacent"` (default) or `"cumulative"`). See Details.
`type`	character: type of DIF to be tested. Either `"both"` for uniform and non-uniform DIF (default), or `"udif"` for uniform DIF only, or `"nudif"` for non-uniform DIF only. 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`	numeric or character: specification of DIF free items. Either `NULL` (default), or a vector of item names (column names of `Data`), or item identifiers (integers specifying the column number) determining which items are currently considered as anchor (DIF free) items. Argument is ignored if `match` is not `"zscore"` or `"score"`.
`purify`	logical: should the item purification be applied? (default is `FALSE`).
`nrIter`	numeric: the maximal number of iterations in the item purification (default is 10).
`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`.
`alpha`	numeric: significance level (default is 0.05).
`parametrization`	deprecated. Use `coef.difORD` for different parameterizations.

Details

Calculates DIF likelihood ratio statistics based either on adjacent category logit model or on cumulative logit model for ordinal data.

Using adjacent category logit model, logarithm of ratio of probabilities of two adjacent categories is

log(P(y = k) / P(y = k - 1)) = b_0k + b_1 * x + b_2k * g + b_3 * x:g,

where x is by default standardized total score (also called Z-score) and g is a group membership.

Using cumulative logit model, probability of gaining at least k points is given by 2PL model, i.e.,

P(y >= k) = exp(b_0k + b_1 * x + b_2k * g + b_3 * x:g) / (1 + exp(b_0k + b_1 * x + b_2k * g + b_3 * x:g)).

The category probability (i.e., probability of gaining exactly k points) is then P(y = k) = P(y >= k) - P(y >= k + 1).

Both models are estimated by iteratively reweighted least squares. For more details see vglm.

Missing values are allowed but discarded for item estimation. They must be coded as NA for both, Data and group parameters.

Value

The difORD() function returns an object of class "difORD". The output including values of the test statistics, p-values, and items marked as DIF is displayed by the print() method.

A list of class "difORD" with the following arguments:

Sval: the values of likelihood ratio test statistics.
ordPAR: the estimates of the final model.
ordSE: standard errors of the estimates of the final model.
parM0: the estimates of null model.
parM1: the estimates of alternative model.
llM0: log-likelihood of null model.
llM1: log-likelihood of alternative model.
AICM0: AIC of null model.
AICM1: AIC of alternative model.
BICM0: BIC of null model.
BICM1: BIC of alternative model.
DIFitems: either the column identifiers of the items which were detected as DIF, or "No DIF item detected" in case no item was detected as DIF.
model: model used for DIF detection.
type: character: type of DIF that was tested.
purification: purify value.
nrPur: number of iterations in item purification process. Returned only if purify is TRUE.
difPur: a binary matrix with one row per iteration of item purification and one column per item. "1" in i-th row and j-th column means that j-th item was identified as DIF in i-th iteration. Returned only if purify is TRUE.
conv.puri: logical indicating whether item purification process converged before the maximal number nrIter of iterations. Returned only if purify is TRUE.
p.adjust.method: character: method for multiple comparison correction which was applied.
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.
alpha: numeric: significance level.
Data: the data matrix.
group: the vector of group membership.
group.names: levels of grouping variable.
match: matching criterion.

For an object of class "difORD" several methods are available (e.g., methods(class = "difORD")).

Author(s)

Adela Hladka (nee Drabinova)
Institute of Computer Science of the Czech Academy of Sciences
Faculty of Mathematics and Physics, Charles University
hladka@cs.cas.cz

Patricia Martinkova
Institute of Computer Science of the Czech Academy of Sciences
martinkova@cs.cas.cz

References

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

Hladka, A. (2021). Statistical models for detection of differential item functioning. Dissertation thesis. Faculty of Mathematics and Physics, Charles University.

Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection. The R Journal, 12(1), 300–323, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32614/RJ-2020-014")}.

Examples

# loading data
data(Anxiety, package = "ShinyItemAnalysis")
Data <- Anxiety[, paste0("R", 1:29)] # items
group <- Anxiety[, "gender"] # group membership variable

# testing both DIF effects with adjacent category logit model
(x <- difORD(Data, group, focal.name = 1, model = "adjacent"))
## Not run: 
# graphical devices
plot(x, item = 6)
plot(x, item = "R6")
plot(x, item = "R6", group.names = c("Males", "Females"))

# estimated parameters
coef(x)
coef(x, SE = TRUE) # with SE
coef(x, SE = TRUE, simplify = TRUE) # with SE, simplified

# AIC, BIC, log-likelihood
AIC(x)
BIC(x)
logLik(x)

# AIC, BIC, log-likelihood for the first item
AIC(x, item = 1)
BIC(x, item = 1)
logLik(x, item = 1)

# testing both DIF effects with Benjamini-Hochberg adjustment method
difORD(Data, group, focal.name = 1, model = "adjacent", p.adjust.method = "BH")

# testing both DIF effects with item purification
difORD(Data, group, focal.name = 1, model = "adjacent", purify = TRUE)

# testing uniform DIF effects
difORD(Data, group, focal.name = 1, model = "adjacent", type = "udif")
# testing non-uniform DIF effects
difORD(Data, group, focal.name = 1, model = "adjacent", type = "nudif")

# testing both DIF effects with total score as matching criterion
difORD(Data, group, focal.name = 1, model = "adjacent", match = "score")

testing both DIF effects with cumulative logit model
(x <- difORD(Data, group, focal.name = 1, model = "cumulative"))
# graphical devices
plot(x, item = 7, plot.type = "cumulative")
plot(x, item = 7, plot.type = "category")

# estimated parameters
coef(x, simplify = TRUE)

## End(Not run)

difNLR documentation built on May 3, 2023, 5:11 p.m.