grt_hm_fit: Fit a hierarchy of traditional GRT models to identification...

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

Description

Fits a hierarchy of traditional GRT models to data from a 2x2 identification experiment, using the BFGS optimization method (See Ashby & Soto, 2015). It then selects the best-fitting model using the AIC.

Usage

grt_hm_fit(cmat, rand_pert = 0.3, n_reps = 10, control = list())

Arguments

cmat	A 4x4 confusion matrix (see Details).
rand_pert	Maximum value of a random perturbation added to the starting parameters. Defaults to 0.3. With a value of zero, the optimization is started exactly at the default starting parameters (see Details). As the value of rand_pert is increased, the starting parameters become closer to be "truly random."
n_reps	Number of times the optimization algorithm should be run, each time with a different value for the starting parameters. The function will return the model with a highest log-likelihood from all the runs. The value of n_reps defaults to ten.
control	A list of optional control parameters for the optim function. See optim. Note that the parameter ndeps entered here should be a single number instead of the vector that is usually passed to optim. This single value is repeated inside grt_hm_fit to create the appropriate vectors.

Details

A 2x2 identification experiment involves two dimensions, A and B, each with two levels, 1 and 2. Stimuli are represented by their level in each dimension (A1B1, A1B2, A2B1, and A2B2) and so are their corresponding correct identification responses (a1b1, a1b2, a2b1, and a2b2).

The data from a single participant in the experiment should be ordered in a 4x4 confusion matrix with rows representing stimuli and columns representing responses. Each cell has the frequency of responses for the stimulus/response pair. Rows and columns should be ordered in the following way:

• Row 1: Stimulus A1B1

• Row 2: Stimulus A2B1

• Row 3: Stimulus A1B2

• Row 4: Stimulus A2B2

• Column 1: Response a1b1

• Column 2: Response a2b1

• Column 3: Response a1b2

• Column 4: Response a2b2

The default starting parameters for the optimization algorithm are the following:

• Means: A1B1=(0,0), A2B1=(1,0), A1B2=(1,0), A2B1=(1,1)

• Variances: All set to one

• Correlations: All set to zero

Decisional separability is assumed for all models (i.e., decision bounds are fixed and orthogonal to the dimension they divide)

Note that a random value will be added to the default starting parameters if rand_pert is given a value higher than zero.

Value

An object of class "grt_hm_fit."

The function summary is used to obtain a summary of results from the model fit and selection process, including the best-fitting model and conclusions about perceptual separability and perceptual independence (decisional separability is assumed by all models)

The function plot is used to print a graphical representation of the best-fitting model.

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 a confusion matrix
# Inside the c(...) below, we enter the data from row 1 in the 
# matrix, then from row 2, etc.
cmat <- matrix(c(140, 36, 34, 40,
                 89, 91, 4, 66,
                 85, 5, 90, 70,
                 20, 59, 8, 163),
                 nrow=4, ncol=4, byrow=TRUE)

# Perform model fit and selection
hm_fit_results <- grt_hm_fit(cmat)

# See a summary of the fitting and selection results
summary(hm_fit_results)

# plot a graphical representation of the best-fitting model
plot(hm_fit_results)

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