grt_wind_fit: Fit a GRT-wIND model to identification data

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

Description

Uses the BFGS optimization method to fit a full GRT-wIND model to data from a 2x2 identification experiment (see Soto et al., 2015).

Usage

grt_wind_fit(cmats, start_params = c(), model = "full",
  rand_pert = 0.3, control = list())

Arguments

cmats	List of confusion matrices. Each entry in the list should contain the 4x4 confusion matrix from one individual (see Details).
start_params	An optional vector of parameters to start the optimization algorithm. You can provide either the group parameters or both group and individual parameters. It will be created automatically if not provided (see Details).
model	A string or vector of strings indicating what GRT-wIND model to run. By default is the full model ("full"), but restricted models can be obtained by combination of several string values. "PS(A)" and "PS(B)" are models that assume PS for dimension A and dimension B, respectively. "PI" is a model that assumes perceptual independence. "DS(A)" and "DS(B)" are models that assume DS for dimension A and dimension B, respectively. "1-VAR" is a model that assumes that all variances are equal to one. A model assuming PS for dimension A and that all variances are equal to one would require setting model=c("PS(A)", "1-VAR").
rand_pert	Maximum value of a random perturbation added to the starting parameters. With a value of zero, the algorithm is started exactly at start_params. As the value of rand_pert is increased, the starting parameters become closer to be "truly random."
control	A list of control parameters for the optim function. See optim.

Details

We recommend that you fit GRT-wIND to your data repeated times, each time with a different value for the starting parameters, and keep the solution with the smallest negative log-likelihood. This facilitates finding the true maximum likelihood estimates of the model's parameters, which is necessary to make valid conclusions about dimensional separability and independence. The function grt_wind_fit_parallel does exactly this, taking advantage of multiple CPUs in your computer to speed up the process. For most applications, you should use grt_wind_fit_parallel instead of the current function.

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 argument cmats is a list with all individual confusion matrices from an experimental group.

If the value of start_params is not provided, the 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

• Decision bounds: All orthogonal to their corresponding dimension

• Attention parameters: No differences in global attention (kappa=2) and no selective attention (lambda=0.5)

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

Value

An object of class "grt_wind_fit."

The function wald is used to obtain the results of Wald tests of perceptual separability, decisional separability and perceptual independence, using the maximum likelihood parameters estimated through grt_wind_fit.

The function summary is used to obtain a summary of the model fit to data and the results of Wald tests (if available). The function plot is used to print a graphical representation of the fitted model.

References

Soto, F. A., Musgrave, R., Vucovich, L., & Ashby, F. G. (2015). General recognition theory with individual differences: A new method for examining perceptual and decisional interactions with an application to face perception. Psychonomic Bulletin & Review, 22(1), 88-111.

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)

# plot a graphical representation of the fitted model
plot(fitted_model)

# optionally, you can run likelihood ratio tests of separability and independence
# (recommended method, but very slow)
fitted_model <- lr_test(fitted_model, cmats)

# alternatively, you can run a Wald test of separability and independence 
# (less recommended method, due to common problems with numerical estimation, but faster)
fitted_model <- wald(fitted_model, cmats)

# print a summary of the fitted model and tests to screen
summary(fitted_model)

# a data frame with the values of all individual parameters is available in
# in fitted_model$indpar
fitted_model$indpar

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