structure.test: Test of covariance structure for PFC models
In ldr: Methods for likelihood-based dimension reduction in regression

Description Usage Arguments Details Author(s) Examples

Information criterion and likelihood ratio test for the structure of the covariance matrix of PFC models.

1	structure.test(object1, object2)

`object1`	An object of class `pfc`
`object2`	A second object of class `pfc`, fitted exactly as for `object1` except for the covariance structure Δ.

Consider two PFC models M_1 and M_2, with the same parameters, except for the conditional covariance that is Δ_1 for M_1 and Δ_2 for M_2 such that model M_1 is nested in model M_2. We implemented the likelihood ratio test for the hypotheses: H_0: Δ=Δ_1 versus H_a: Δ=Δ_2. The test is implemented for the isotropic, anisotropic, and the unstructured PFC models. One may test isotropic against either anisotropic or unstructured, or test anisotropic against unstructured. The degrees of freedom are given by the difference in the number of parameters in the covariances. Information criterion AIC and BIC are also provided.

Kofi Placid Adragni <kofi@umbc.edu>

data(bigmac)
fit1 <- pfc(X=bigmac[,-1], y=bigmac[,1], fy=bf(y=bigmac[,1], case="poly", 
        degree=3), numdir=3, structure="iso")
fit2 <- pfc(X=bigmac[,-1], y=bigmac[,1], fy=bf(y=bigmac[,1], case="poly", 
        degree=3), numdir=3, structure="aniso")
fit3 <- pfc(X=bigmac[,-1], y=bigmac[,1], fy=bf(y=bigmac[,1], case="poly", 
        degree=3), numdir=3, structure="unstr")
structure.test(fit1, fit3)
structure.test(fit2, fit3)

Loading required package: GrassmannOptim
Loading required package: Matrix

Likelihood Ratio Test:
NH: structure= iso 
AH: structure= unstr 
     Stat df p.value
 1504.756 44       0

Information Criteria:
         iso    unstr
aic 4543.674 3126.919
bic 4610.521 3273.258

Likelihood Ratio Test:
NH: structure= aniso 
AH: structure= unstr 
     Stat df p.value
 253.0225 36       0

Information Criteria:
       aniso    unstr
aic 3307.941 3126.919
bic 3389.241 3273.258