DIF analysis via Andersen's likelihood-ratio test

Splits a Rasch model by an external grouping variable using eRm::LRtest() and reports per-group item locations (or per-group threshold locations) together with their standard errors. A single function replaces the four legacy helpers (RIdifTableLR, RIdifThreshTblLR, RIdifFigureLR, RIdifThreshFigLR) by exposing the two underlying axes – level (item or threshold) and output (data.frame, kable, or ggplot) – as arguments. The same data preparation pipeline feeds all six combinations.

Usage

RMdifLR(
  data,
  dif_var,
  model = c("auto", "PCM", "RM"),
  level = c("item", "threshold"),
  output = c("ggplot", "kable", "dataframe"),
  cutoff = 0.5,
  conf = 0.95,
  sort = FALSE
)

Arguments

data: A data.frame or matrix of item responses (non-negative integers, 0-based). One column per item, one row per person. Person IDs and grouping variables must not be included – pass the grouping variable separately via dif_var.
dif_var: Vector of length nrow(data) (factor, character, or numeric) defining the DIF grouping variable. Coerced to factor; unused levels are dropped. Rows where dif_var is NA are dropped with a message. Must result in at least 2 groups after cleaning.
model: One of "auto" (default), "PCM", or "RM". "auto" fits eRm::RM() when the data are dichotomous (max response = 1) and eRm::PCM() otherwise. "RM" errors on polytomous data.
level: One of "item" (default) or "threshold". "item" reports each item's mean threshold location per group; "threshold" reports each individual threshold per group. For dichotomous (RM) data the two views are equivalent (one threshold per item).
output: One of "ggplot" (default), "kable", or "dataframe". The data.frame view always carries a Flagged logical column; the kable view bolds flagged rows; the ggplot view shows confidence intervals.
cutoff: Numeric or NULL. Threshold (in logits) for the Flagged column: a row is flagged when MaxDiff > cutoff, where MaxDiff is the difference between the largest and smallest per-group location for that item (or threshold). Set to NULL to suppress flagging. Default 0.5.
conf: Numeric in (0, 1). Confidence level used for the ggplot error bars. Default 0.95.
sort: Logical. kable output only: sort rows by MaxDiff (descending). Default FALSE.

Value

A data.frame, a knitr_kable object, or a ggplot object, depending on output.

The data.frame has one row per item (level = "item") or per item x threshold (level = "threshold"), with columns Item (and Threshold at threshold level), one numeric column per group level, an All column for the unsplit fit, MaxDiff, Flagged (when cutoff is non-NULL), and matching SE_* columns.

The Andersen LR test result is attached as attr(result, "lr_test") on the data.frame, in the kable footnote, and in the ggplot caption (LR \(\chi^2\), df, p-value).

Details

The Partial Credit Model (PCM) is fitted by default for polytomous data and the dichotomous Rasch Model (RM) is fitted when all responses are 0/1; this can be overridden via model.

For the data.frame and kable outputs, locations are reported on the centred eRm parameterisation returned by eRm::thresholds(). Per-group fits come from eRm::LRtest(..., splitcr = dif_var); the unsplit fit (All column) is the model fitted to the full dataset. The Andersen LR statistic, df, and p-value reported as the lr_test attribute / caption come directly from LRtest()'s return value.

cell_spec()-style HTML cell colouring used in the legacy easyRasch package has been dropped in favour of a logical Flagged column (and bold rendering in the kable output), so the kable renders correctly in HTML, LaTeX, and pipe/markdown.

Examples

# \donttest{
set.seed(1)
data("pcmdat2", package = "eRm")
grp <- factor(sample(c("A", "B"), nrow(pcmdat2), replace = TRUE))

# Default: ggplot panel of item locations with 95% CIs
RMdifLR(pcmdat2, dif_var = grp)


# Threshold-level kable, sorted by MaxDiff
RMdifLR(pcmdat2, dif_var = grp,
        level = "threshold", output = "kable", sort = TRUE)
#> 
#> 
#> Table: Partial Credit Model split by DIF variable (2 groups). Andersen LR chi^2 = 4.064, df = 7, p = 0.772. n = 300 complete cases, 4 items. **Bold** = MaxDiff > 0.5 logits.
#> 
#> |Item |Threshold |      A|      B|    All| MaxDiff|Flagged |  SE_A|  SE_B| SE_All|
#> |:----|:---------|------:|------:|------:|-------:|:-------|-----:|-----:|------:|
#> |I1   |c1        |  0.130| -0.346| -0.104|   0.476|no      | 0.214| 0.219|  0.152|
#> |I1   |c2        |  1.965|  2.367|  2.180|   0.402|no      | 0.288| 0.282|  0.201|
#> |I4   |c1        | -1.096| -0.865| -0.983|   0.231|no      | 0.294| 0.282|  0.203|
#> |I4   |c2        |  0.996|  0.789|  0.889|   0.206|no      | 0.234| 0.235|  0.165|
#> |I3   |c1        | -2.409| -2.228| -2.315|   0.182|no      | 0.506| 0.452|  0.336|
#> |I2   |c2        |  2.086|  1.922|  1.996|   0.164|no      | 0.309| 0.291|  0.211|
#> |I3   |c2        |  0.657|  0.543|  0.597|   0.114|no      | 0.225| 0.224|  0.158|
#> |I2   |c1        |  0.524|  0.629|  0.571|   0.104|no      | 0.210| 0.211|  0.148|

# Tidy data.frame for downstream use
df <- RMdifLR(pcmdat2, dif_var = grp, output = "dataframe")
attr(df, "lr_test")
#> $LR
#> [1] 4.063775
#> 
#> $df
#> [1] 7
#> 
#> $p_value
#> [1] 0.7724031
#> 
#> $n_groups
#> [1] 2
#> 
#> $groups
#> [1] "A" "B"
#> 
#> $model
#> [1] "PCM"
#> 
#> $n_persons
#> [1] 300
#> 
#> $n_items
#> [1] 4
#> 
df[df$Flagged, ]
#> [1] Item    A       B       All     MaxDiff Flagged SE_A    SE_B    SE_All 
#> <0 rows> (or 0-length row.names)
# }