lr_test: Run likelihood ratio tests of separability and independence

In fsotoc/grtools: General Recognition Theory tools for the analysis of perceptual independence

Description

Run likelihood ratio tests of perceptual separability, decisional separability, and perceptual independence (see Ashby & Soto, 2015), using the maximum likelihood parameter estimates stored in a grt_wind_fit object. The method considers any restrictions placed in the original model and stored in grt_wind_fit$restrictions.

Usage

lr_test(fitted_model, cmats, n_reps=20, test=c("PS(A)", "PS(B)", "PI", "DS(A)", "DS(B)"))

Arguments

fitted_model	An object returned by grt_wind_fit or grt_wind_fit_parallel
cmats	List of confusion matrices. Each entry in the list should contain the 4x4 confusion matrix from one individual. For a detailed description of how to create this list, see grt_wind_fit
n_reps	Number of times the optimization algorithm should be run when a restricted model is fitted to the data (see Details).
test	A string array indicating the test(s) to be performed. "PS(A)" and "PS(B)" indicate to test perceptual separability of A and B, respectively. "PI" indicates to test perceptual independence. "DS(A)" and "DS(B)" indicate to test decisional separability of A and B, respectively. The default is test=c("PS(A)", "PS(B)", "PI", "DS(A)", "DS(B)"), which includes all tests.

Details

Each likelihood ratio test involves fitting a restricted model to the data (e.g., a model in which parameters are fixed to reflect PS) and then statistically comparing the fit of the restricted model against that of the full model (for details, see Ashby & Soto, 2015). The lr_test function calls grt_wind_fit_parallel to fit a restricted model several times (determined by parameter n_reps; set to 20 by default). Each time, the starting parameter values are the values previously found by fitting the full model, with small random values added or subtracted (for details about the fitting procedure, see grt_wind_fit). The best-fitting model is chosen and used in the likelihood ratio test.

Because likelihood ratio tests require fitting a GRT-wIND model many times, you should expect the analysis to take considerable time to finish. We recommend you to run only the tests that interest you, and not all the tests included by default.

Value

An object of class "grt_wind_fit," including information about likelihood ratio tests.

The function summary is used to obtain a summary of the model fit to data and the results of likelihood ratio tests.

References

Ashby, F. G., & Soto, F. A. (2015). Multidimensional signal detection theory. In J. R. Busemeyer, J. T. Townsend, Z. J. Wang, & A. Eidels (Eds.), Oxford handbook of computational and mathematical psychology (pp. 13-34). Oxford University Press: New York, NY.

Examples

# Create list with confusion matrices. In this example, we enter data from
# an experiment with 5 participants. For each participant, inside the c(...),
# enter the data from row 1 in the matrix, then from row 2, etc.
cmats <- list(matrix(c(161,41,66,32,24,147,64,65,37,41,179,43,14,62,22,202),nrow=4,ncol=4,byrow=TRUE))
cmats[[2]] <- matrix(c(126,82,67,25,8,188,54,50,34,75,172,19,7,103,14,176),nrow=4,ncol=4,byrow=TRUE)
cmats[[3]] <- matrix(c(117,64,89,30,11,186,69,34,21,81,176,22,10,98,30,162),nrow=4,ncol=4,byrow=TRUE)
cmats[[4]] <- matrix(c(168,57,47,28,15,203,33,49,58,54,156,32,9,96,9,186),nrow=4,ncol=4,byrow=TRUE)
cmats[[5]] <- matrix(c(169,53,53,25,34,168,69,29,38,48,180,34,19,44,60,177),nrow=4,ncol=4,byrow=TRUE)

# fit the model to data
fitted_model <- grt_wind_fit(cmats)

#' # run the likelihood ratio tests
fitted_model <- lr_test(fitted_model, cmats)

# see the results
summary(fitted_model)

fsotoc/grtools documentation built on Nov. 15, 2020, 5:14 a.m.