IRT moment linking (mean/mean, mean/sigma)

Estimates the linear transformation theta_T = A theta_F + B from common-item slope/difficulty parameters: mean/mean uses A = mu(a_F)/mu(a_T); mean/sigma uses A = sd(b_T)/sd(b_F); both use B = mu(b_T) - A mu(b_F). The transformed from-scale parameters a* = a_F/A, b* = A b_F + B are also returned.

Usage

morie_linkmm(a_from, b_from, a_to, b_to, method = "mean/mean")

Arguments

a_from, b_from: Numeric vectors of common-item parameters on the from scale.
a_to, b_to: The same items' parameters on the to scale.
method: "mean/mean" (default) or "mean/sigma".

Value

A list with elements A, B, a_transformed, b_transformed, n_common, method.

References

Weeks, J. P. (2010). plink: An R package for linking mixed-format tests using IRT-based methods. Journal of Statistical Software, 35(12). Marco, G. L. (1977). Journal of Educational Measurement, 14, 139-160. Loyd, B. H. and Hoover, H. D. (1980). Journal of Educational Measurement, 17, 179-193.

Examples

morie_linkmm(a_from = c(1, 2, 3, 4, 5, 6, 7, 8), b_from = c(1, 2, 3, 4, 5, 6, 7, 8),
  a_to = c(1, 2, 3, 4, 5, 6, 7, 8), b_to = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $A
#> [1] 1
#> 
#> $B
#> [1] 0
#> 
#> $a_transformed
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $b_transformed
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $n_common
#> [1] 8
#> 
#> $method
#> [1] "IRT moment linking (mean/mean; plink Eqs. 12-13)"
#>