# lagrange: Lagrange test for freeing parameters In mirt: Multidimensional Item Response Theory

## Description

Lagrange (i.e., score) test to test whether parameters should be freed from a more constrained baseline model.

## Usage

 `1` ```lagrange(mod, parnum, SE.type = "Oakes", type = "Richardson", ...) ```

## Arguments

 `mod` an estimated model `parnum` a vector, or list of vectors, containing one or more parameter locations/sets of locations to be tested. See objects returned from `mod2values` for the locations `SE.type` type of information matrix estimator to use. See `mirt` for further details `type` type of numerical algorithm passed to `numerical_deriv` to obtain the gradient terms `...` additional arguments to pass to `mirt`

## Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

## References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi: 10.18637/jss.v048.i06

`wald`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33``` ```## Not run: dat <- expand.table(LSAT7) mod <- mirt(dat, 1, 'Rasch') (values <- mod2values(mod)) #test all fixed slopes individually parnum <- values\$parnum[values\$name == 'a1'] lagrange(mod, parnum) # compare to LR test for first two slopes mod2 <- mirt(dat, 'F = 1-5 FREE = (1, a1)', 'Rasch') coef(mod2, simplify=TRUE)\$items anova(mod, mod2) mod2 <- mirt(dat, 'F = 1-5 FREE = (2, a1)', 'Rasch') coef(mod2, simplify=TRUE)\$items anova(mod, mod2) mod2 <- mirt(dat, 'F = 1-5 FREE = (3, a1)', 'Rasch') coef(mod2, simplify=TRUE)\$items anova(mod, mod2) # test slopes first two slopes and last three slopes jointly lagrange(mod, list(parnum[1:2], parnum[3:5])) # test all 5 slopes and first + last jointly lagrange(mod, list(parnum[1:5], parnum[c(1, 5)])) ## End(Not run) ```