lr_test function

Likelihood ratio test for a linear model, based on RRPP

Function performs likelihood ratio tests on an lm.rrpp fit, using RRPP or FRPP. Likelihood ratio statistics are calculated for every random permutation, and the effect size is estimated from the distribution of random statistics. The likelihood ratio tests has some resemblance to MANOVA, especially using Wilks' lambda. Sums of squares and cross-products (SSCP) matrices are calculated over the random permutations of a lm.rrpp fit. SSCP matrices are computed, as are the inverse of R times H (invR.H), where R is a SSCP for the residuals or random effects and H is the difference between SSCP matrices of full and reduced models (see manova.update). From invR.H, Wilks lambda is first estimated, and the likelihood ratio stat is then estimated as -n * log(Wilks).

This function does one of two things. It either performs an update using manova.update, using Wilks' lambda as the test statistic, converting Wilks' lambda to likelihood ratio statistics or it uses the results from a previously performed update to calculate new statistics.

lr_test(fit, verbose = FALSE, ...)

Arguments

• fit: Linear model fit from lm.rrpp or a fit that has already been updated with manova.update.
• verbose: Logical value for whether to include all random Wilks' lambda and likelihood ratio statistics from random permutations.
• ...: Arguments passed onto manova.update.

Examples

# Body Shape Analysis (Multivariate) ----------------

## Not run:

data(Pupfish)

# Although not recommended as a practice, this example will use only
# three principal components of body shape for demonstration.  
# A larger number of random permutations should also be used.

Pupfish$shape <- ordinate(Pupfish$coords)$x[, 1:3]

fit <- lm.rrpp(shape ~ log(CS) + Sex, SS.type = "I", 
data = Pupfish, print.progress = FALSE, iter = 499) 
summary(fit, formula = FALSE)
anova(fit) # ANOVA table

# MANOVA

fit.m <- manova.update(fit, print.progress = FALSE, tol = 0.001)
summary(fit.m, test = "Roy")
summary(fit.m, test = "Wilks")

# Likelihood Ratio Test

LRT <- lr_test(fit.m)
summary(LRT)
## End(Not run)

References

Adams, D. C., and M. L. Collyer. 2024. Extended phylogenetic regression models for comparing within-species patterns across the tree of life. Methods in Ecology and Evolution. In review.

Author(s)

Michael Collyer