delta_mean_item: Expected bias to item mean
In dmacs: Measurement Nonequivalence Effect Size Calculator

Description Usage Arguments Details Value References Examples

delta_mean_item computes the expected bias in item mean due to measurement nonequivalence.

1 2	delta_mean_item(LambdaR, ThreshR, LambdaF, ThreshF, MeanF, VarF, categorical = FALSE, stepsize = 0.001)

`LambdaR`	is the factor loading of the item onto the factor of interest for the reference group.
`ThreshR`	is the indicator intercept (for continuous indicators) or a vector of thresholds (for categorical indicators) for the reference group.
`LambdaF`	is the factor loading of the item onto the factor of interest for the focal group.
`ThreshF`	is the indicator intercept (for continuous indicators) or a vector of thresholds (for categorical indicators) for the focal group.
`MeanF`	is the factor mean in the focal group
`VarF`	is the factor variances in the focal group.
`categorical`	is a Boolean variable declaring whether the variables in the model are ordered categorical. Models in which some variables are categorical and others are continuous are not supported. If no value is provided, categorical defaults to `FALSE`, although if a vector of thresholds are provided, categorical will be forced to `TRUE`. A graded response model with probit link (e.g., DWLS in lavaan or WLSMV in Mplus) is used for categorical variables. If you desire for other categorical models (e.g., IRT parameterization) to be supported, e-mail the maintainer.
`stepsize`	is the interval width for the Riemann sum used to estimate the integral in equation 6 of Nye & Drasgow (2011). Default value is .001. A larger value can be used for faster performance; accuracy is excellent at `stepsize = .01` in my simulations.

delta_mean_item is called by dmacs_summary_single, which in turn is called by lavaan_dmacs and mplus_dmacs, which are the only functions in this package intended for casual users

The expected bias in item mean due to measurement nonequivalence in equation 4 of Nye & Drasgow (2011).

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.

LambdaF <- 0.74
LambdaR <- 0.76
ThreshF <- 1.28
ThreshR <- 0.65
MeanF   <- 0.21
VarF    <- 1.76
delta_mean_item(LambdaR, ThreshR, LambdaF, ThreshF, MeanF, VarF)