difR (version 6.1.0)

difMantel.poly: Mantel Differential Item Functioning Detection for Polytomous Items

Description

Implements Mantel's (1963) chi-square test for detecting DIF in polytomous (ordinal) items, with optional iterative purification and Liu–Agresti (1996) cumulative common odds ratios per item.

Usage

difMantel.poly(data, group, focal.name, ref.name,
               match = "score", sig.level = 0.05,
               purify = FALSE, max.iter = 10)

Value

A data.frame with one row per item and the following columns:

Stat

Mantel chi-square statistic (1 df), conditioning on the chosen matching score.

p.value

Associated p-value.

p.adj

Holm-adjusted p-value across items.

Psi_hat

Liu–Agresti cumulative common odds ratio estimate \(\hat\Psi\).

Alpha_hat

\(\log(\hat\Psi)\).

SE_log_Psi

Standard error of \(\log(\hat\Psi)\) (large-sample Liu–Agresti).

rho.spear

Spearman correlation between the item score and the matching score (score or restscore).

LA.valid

Logical flag indicating whether Liu–Agresti estimates were computable for the item (e.g., sufficient data in both groups across strata).

Arguments

data

Matrix or data frame of polytomous item responses (one row per subject, one column per item).

group

Vector or factor indicating group membership (same length as nrow(data)). The function internally reorders levels so that ref.name is the reference and focal.name the focal group.

focal.name

Value in group corresponding to the focal group.

ref.name

Value in group corresponding to the reference group.

match

Matching variable: "score" (total score) or "restscore" (total score excluding the tested item).

sig.level

Significance level used during purification (default 0.05).

purify

Logical. If TRUE and match="score", performs iterative purification by removing flagged items from the anchor set until convergence or max.iter is reached. Ignored when match="restscore".

max.iter

Maximum number of purification iterations (default 10).

Author

Sebastien Beland\ Faculte des sciences de l'education, Université de Montreal (Canada)\

Details

For each item, the Mantel statistic is computed on ordinal responses while conditioning on a matching score. When match="score", the total test score is used; when match="restscore", the current item is excluded from the matching score to reduce contamination.

Cumulative common odds ratios (Liu & Agresti, 1996) are computed conditional on the same strata (the matching score) and reported along with their standard errors via the Liu–Agresti delta method. Internally, the function coerces group to have levels c(ref.name, focal.name) to ensure coherent sign/orientation of \(\log(\Psi)\).

When purify=TRUE (and match="score"), the anchor set excludes items flagged as DIF at level sig.level. Iterations stop when the set stabilizes or max.iter is reached. The final result is returned, with attributes "iterations" and "final_anchors" set when purification was performed.

Notes. (i) Liu–Agresti estimates are computed only when both groups are observed within strata with sufficient counts; otherwise LA.valid=FALSE. (ii) Missing responses should be handled prior to analysis (e.g., listwise deletion); this function does not impute missing values.

References

Mantel, N. (1963). Chi-square tests with one degree of freedom: Extensions of the Mantel–Haenszel procedure. Journal of the American Statistical Association, 58, 690–700.

Liu, I., & Agresti, A. (1996). Mantel–Haenszel-type inference for cumulative odds ratios with a stratified ordinal response. Biometrics, 52(4), 1223–1234.

See Also

liu_agresti_ccor, mantelhaen.test

Examples

if (FALSE) {
# Real data example
data(SCS)
# Without purification
difMantel.poly(data = SCS[, 1:10], group = SCS$Gender, focal.name = 1, 
ref.name = 2, purify = FALSE)

# Without purification and restscore
difMantel.poly(data = SCS[, 1:10], group = SCS$Gender, focal.name = 1, 
ref.name = 2, purify = TRUE,match = "restscore")

# With purification
difMantel.poly(data = SCS[, 1:10], group = SCS$Gender, focal.name = 1, 
ref.name = 2, purify = TRUE)

# With simulated data

set.seed(1234)

# original item parameters
a <- rlnorm(10, -0.5)  # slopes
b <- runif(10, -2, 2)  # difficulty
d <- list()
d[[1]] <- c(0, 2, .5, -.15, -1.1)
d[[2]] <- c(0, 2, .25, -.45, -.75)
d[[3]] <- c(0, 1, .5, -.65, -1)
d[[4]] <- c(0, 2, .5, -.85, -2)
d[[5]] <- c(0, 1, .25, -.05, -1)
d[[6]] <- c(0, 2, .5, -.95, -1)
d[[7]] <- c(0, 1, .25, -.35, -2)
d[[8]] <- c(0, 2, .5, -.15, -1)
d[[9]] <- c(0, 1, .25, -.25, -2)
d[[10]] <- c(0, 2, .5, -.35, -1)

# Uniform DIF
It <- 10; NR <- 1000; NF <- 1000
ItDIFa <- NULL; Ga <- NULL
ItDIFb <- c(1, 3)
Gb <- rep(.5, 2)

Out.Unif <- SimPolyDif(It, ItDIFa, ItDIFb, NR, NF, a, b, d,
                       ncat = 5, Ga = Ga, Gb = Gb)
Out.Unif$ipars
Data <- Out.Unif$data

# Without purification and rest score
difMantel.poly(data = Data[, 1:10], group = Data$group, focal.name = "G1", 
ref.name = "G2", purify = FALSE,match = "restscore")

# With purification
difMantel.poly(data = Data[, 1:10], group = Data$group, focal.name = "G1", 
ref.name = "G2", purify = TRUE)

# We implemented a specific S3 plot method: plot.Logistic. It can be used as follows:
res <- difMantel.poly(data = Data[, 1:10], group = Data$group, focal.name = "G1", 
ref.name = "G2", purify = FALSE)
plot.MHPoly(res)
}