difNLR (version 1.3.0)

formulaNLR: Formula for Non-Linear Regression DIF model.

Description

Function returns the formula of the non-linear models based on model specification and DIF type to be tested.

Usage

formulaNLR(model, constraints = NULL, type = "both", parameterization = "classic",
outcome)

Arguments

model

character: generalized logistic regression model to be fitted. See Details.

constraints

character: which parameters should be the same for both groups. Default value is NULL. See Details.

type

character: type of DIF to be tested. Possible values are "both" (default), "udif", "nudif", "all", or combination of parameters 'a', 'b', 'c' and 'd'. See Details.

parameterization

character: which parameterization should be used. Possible values are "classic" (default) and "alternative". See Details.

outcome

character: name of outcome to be printed in formula. If not specified 'y' is used.

Value

A list of two models. Both includes formula, parameters to be estimated and their lower and upper constraints.

Details

The unconstrained form of 4PL generalized logistic regression model for probability of correct answer (i.e., y = 1) is P(y = 1) = (c + cDif*g) + (d + dDif*g - c - cDif*g)/(1 + exp(-(a + aDif*g)*(x - b - bDif*g))), where x is standardized total score (also called Z-score) and g is group membership. Parameters a, b, c and d are discrimination, difficulty, guessing and inattention. Parameters aDif, bDif, cDif and dDif then represetn differences between two groups in discrimination, difficulty, guessing and inattention.

This 4PL model can be further constrained by model and constraints arguments. The arguments model and constraints can be also combined.

The model argument offers several predefined models. The options are as follows: Rasch for 1PL model with discrimination parameter fixed on value 1 for both groups, 1PL for 1PL model with discrimination parameter fixed for both groups, 2PL for logistic regression model, 3PLcg for 3PL model with fixed guessing for both groups, 3PLdg for 3PL model with fixed inattention for both groups, 3PLc (alternatively also 3PL) for 3PL regression model with guessing parameter, 3PLd for 3PL model with inattention parameter, 4PLcgdg for 4PL model with fixed guessing and inattention parameter for both groups, 4PLcgd (alternatively also 4PLd) for 4PL model with fixed guessing for both groups, 4PLcdg (alternatively also 4PLc) for 4PL model with fixed inattention for both groups, or 4PL for 4PL model.

The model can be specified in more detail with constraints argument which specifies what arguments should be fixed for both groups. For example, choice 'ad' means that discrimination (a) and inattention (d) are fixed for both groups and other parameters (b and c) are not.

The type corresponds to type of DIF to be tested. Possible values are "both" to detect any DIF caused by difference in difficulty or discrimination (i.e., uniform and/or non-uniform), "udif" to detect only uniform DIF (i.e., difference in difficulty b), "nudif" to detect only non-uniform DIF (i.e., difference in discrimination a), or "all" to detect DIF caused by difference caused by any parameter that can differed between groups. The type of DIF can be also specified in more detail by using combination of parameters a, b, c and d. For example, with an option 'c' for 4PL model only the difference in parameter c is tested.

For an option "alternative" in parameterization argument, all models with the different guessing or/and inattention parameters are reparameterized as follows: P(y = 1) = (cR*(1-g) + cF*g) + (dR*(1-g) + dF*g - cR*(1-g) - cF*g)/(1 + exp(-(a + aDif*g)*(x - b - bDif*g))).

See Also

difNLR

Examples

# NOT RUN {
# 3PL model with the same guessing for both groups
# to test both types of DIF
formulaNLR(model = "3PLcg", type = "both")

# 4PL model with the same guessing and inattention
# to test uniform DIF
formulaNLR(model = "4PLcgdg", type = "udif")

# 2PL model to test non-uniform DIF
formulaNLR(model = "2PL", type = "nudif")

# 4PL model to test all possible DIF
# with alternative parameterization
formulaNLR(model = "4PL", type = "all", parameterization = "alternative")

# 4PL model with fixed a and c parameter
# to test difference in b with alternative parameterization
formulaNLR(model = "4PL", constraints = "ac", type = "b", parameterization = "alternative")
# }
# NOT RUN {
# }