chi2 = (vR - vF)' (SigR + SigF)^-1 (vR - vF) on p df, p being the
number of parameters compared. The covariances ADD because the two
groups are independent samples.
Usage
morie_lord_chisq(b_R, b_F, V_R, V_F = NULL)
Arguments
- b_R, b_F
item parameter estimates in reference and focal groups.
- V_R
covariance of b_R, or the already-summed covariance if
V_F is omitted.
- V_F
covariance of b_F, optional.
Value
list: statistic, pvalue, df, difference, method.
Details
This presumes the estimates are already on a common metric. IRT
parameters are identified only up to a linear transformation of
theta, so without linking a significant result may be reporting the
scale difference rather than DIF. No arithmetic here can detect that.
References
Lord, F. M. (1980), ch. 14. Cross-checked against
LordChi2 in the difR package.
Examples
morie_lord_chisq(0.4, 0.1, matrix(0.04), matrix(0.09))$statistic
#> [1] 0.6923077
