Thurstone-Mosteller Model (Case V)

Fits a Thurstone-Mosteller model (Case V) by maximum likelihood.

thurstone(M)

Arguments

M

a square matrix or a data frame consisting of absolute choice frequencies; row stimuli are chosen over column stimuli

Details

thurstone provides a front end for glm. See Critchlow and Fligner (1991) for more details.

Value

estimate

a vector of parameter estimates (scale values), first element is set to zero

goodness.of.fit

the goodness of fit statistic including the likelihood ratio fitted vs. saturated model (-2logL), the degrees of freedom, and the p-value of the corresponding chi-square distribution

tm.glm

the output from a call to glm

References

Critchlow, D.E., & Fligner, M.A. (1991). Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation in GLIM. Psychometrika, 56, 517–533. doi:10.1007/bf02294488

See also

eba, strans, pcX, kendall.u, circular, glm.

Examples

## Taste data (David, 1988, p. 116)
taste <- matrix(c( 0,  3,  2,  2,
                  12,  0, 11,  3,
                  13,  4,  0,  5,
                  13, 12, 10,  0), 4, 4, byrow=TRUE)
dimnames(taste) <- setNames(rep(list(c("A1", "A2", "A3", "A4")), 2),
                            c(">", "<"))
thurstone(taste)  # Thurstone-Mosteller model fits OK
#> 
#> Thurstone-Mosteller model (Case V)
#> 
#> Parameter estimates:
#>     A1      A2      A3      A4  
#> 0.0000  0.9453  0.7682  1.3874  
#> 
#> Goodness of fit (-2 log likelihood ratio):
#> 	G2(3) = 4.533, p = 0.2094
#>