dmacs: Compute dMACS effect size described in Nye & Drasgow (2011)...

In marklhc/pinvsearch: Specification search for partial factorial invariance

Compute dMACS effect size described in Nye & Drasgow (2011) for two groups.

Description

dmacs returns the dMACS effect size statistics given a set of loadings and intercepts.

Usage

dmacs(
  intercepts,
  loadings = NULL,
  pooled_item_sd = NULL,
  latent_mean = 0,
  latent_sd = 1,
  uniqueness = NULL,
  ns = NULL,
  item_weights = NULL
)

dmacs_ordered(
  thresholds,
  loadings,
  thetas = 1,
  link = c("probit", "logit"),
  pooled_item_sd = NULL,
  latent_mean = 0,
  latent_sd = 1,
  item_weights = NULL
)

Arguments

intercepts	A 2 \times p matrix of measurement intercepts.
loadings	A 2 \times p matrix of factor loadings, where p is the number of items.
pooled_item_sd	A numeric vector of length p of the pooled standard deviation (SD) of the items across groups.
latent_mean	latent factor mean for the reference group. Default to 0.
latent_sd	latent factor SD for the reference group. Default to 1.
uniqueness	A vector of length p of uniqueness.
ns	A vector of length p of sample sizes.
item_weights	Default is NULL. Otherwise, one can specify a vector of length p of weights; if so, test-level dMACS will be computed.
thresholds	A matrix with two rows for measurement thresholds. The matrix must have column names indicating to which item index each column corresponds.
thetas	Not currently used.
link	Link function for the model (probit or logit).

Details

The d_\text{MACS} effect size is defined as (Nye & Drasgow, 2011, p. 968)

d_{\text{MACS}, i} = \frac{1}{\mathit{SD}_{iP}} \sqrt{\int [(\nu_{iR} - \nu{iF}) + (\lambda_{iR} - \lambda_{iF}) \eta]^2 f(\eta) d \eta}

where \lambda is the loading and \nu is the intercept, F and R denote the focal and the reference group. The effect size reflects the standardized mean difference on an item due to measurement noninvariance, and is analogous to the Cohen's d effect size.

Value

A 1 x p matrix of dMACS effect size. If item_weights is not NULL, p = 1.

References

Nye, C. & Drasgow, F. (2011). Effect size indices for analyses of measurement equivalence: Understanding the practical importance of differences between groups. Journal of Applied Psychology, 96(5), 966-980.

Examples

lambdaf <- c(.8, .5, .7, .5)
lambdar <- c(.8, .5, .4, .6)
nuf <- c(0.1, 0, 0.2, 0)
nur <- c(0.2, 0, 0, 0)
dmacs(rbind(nuf, nur),
      loadings = rbind(lambdaf, lambdar),
      pooled_item_sd = c(1, 1, 1, 1),
      latent_mean = 0,
      latent_sd = 1)
dmacs(rbind(nuf, nur),
      loadings = rbind(lambdaf, lambdar),
      pooled_item_sd = c(1, 1, 1, 1),
      latent_mean = 0,
      latent_sd = 1,
      item_weights = c(1, 1, 1, 1))
# Thresholds
lambda <- rbind(c(.8, .5, .7, .5),
                c(.8, .5, .4, .6))
tau <- rbind(c(-0.5, 0, 1, -0.3, 0.1, 0.5, -0.5, 1.5),
             c(-0.5, 0, 1, -0.5, 0.3, 0.5, -1, 1.5))
# three thresholds for items 1 and 2; one threshold for items 3 and 4
colnames(tau) <- c(1, 1, 1, 2, 2, 2, 3, 4)
dmacs_ordered(tau,
              loadings = lambda,
              pooled_item_sd = c(1, 1, 1, 1),
              latent_mean = 0,
              latent_sd = 1)

marklhc/pinvsearch documentation built on June 11, 2025, 6:43 a.m.