Fit the mean and covariance of a bivariate Gaussian distribution for each stimulus class, subject to given constraints.
Standard case uses confusion matrix from a 2x2 full-report identification experiment, but will also work in designs with N levels of confidence associated with each dimension (e.g. in Wickens, 1992).
Can be entered in two ways: 1) a 4x4 confusion matrix containing counts,
with each row corresponding to a stimulus and each column corresponding to a response.
row/col order must be a_1b_1, a_1b_2, a_2b_1, a_2b_2.
2) A three-way 'xtabs' table with the stimuli as the third index and the
NxN possible responses as the first two indices.
PS_x
if TRUE, will fit model with assumption of perceptual separability on the x dimension (FALSE by default)
PS_y
if TRUE, will fit model with assumption of perceptual separability on the y dimension (FALSE by default)
PI
'none' by default, imposing no restrictions and fitting different correlations for all distributions.
If 'same_rho', will constrain all distributions to have same correlation parameter.
If 'all', will constain all distribution to have 0 correlation.
method
The optimization method used to fit the Gaussian model. Newton-Raphson gradient descent by default, but
may also specify any method available in optim, e.g. "BFGS".
Value
An S3 grt object
Examples
# Fit unconstrained model
data(thomas01b);
grt_obj <- fit.grt(thomas01b);
# Use standard S3 generics to examine
print(grt_obj);
summary(grt_obj);
plot(grt_obj);
# Fit model with assumption of perceptual separability on both dimensions
grt_obj_PS <- fit.grt(thomas01b, PS_x = TRUE, PS_y = TRUE);
summary(grt_obj_PS);
plot(grt_obj_PS);
# Compare models
GOF(grt_obj, teststat = 'AIC');
GOF(grt_obj_PS, teststat = 'AIC');
providing 
.