# Statistical tests of significance for effects

For fixed effects and covariates, HIBLUP can do statistical test automatically, and list the results in file *.anova, the p-value of F test at the last column could be used as a diagnosis of which fixed effects or covariates are statistically significant for a trait.

For random effect (genetic or environmental), there is no automatic function of statistical test for significance, users can achieve it manually by the Likelihood Ratio Test (LRT) following the steps below:

(1) run full model with the random effect of interest, get the loglike value L1 (which can be found from the LOG information of HIBLUP at the last iteration of REML).

(2) run reduced model in which the random effect of interest is dropped off, get the loglike value L0.

(3) calculate the p-value by Chi-square test in R:

> stat <- 2 * (L1 - L0)
> pvaue <- pchisq(stat, df = 1, lower.tail = FALSE)
> print(pvaue)