Variance Test For General Linear Models With Individual Random Effects

In biology and genetics stduies,in order to understand the impact of biological be-havior on the overall and genetic diseases on organisms,people often use longitudinal data to analyze the biological behavior at different periods and the contagion risk of genetic diseases.The usual solution based on the co-random effect hypothesis,that the random effects of all objects are the same.it is not difficult to find that the quality of an individual can affect the overall effect in the studies,more generally,it is difficult to test from the mixed effect model.So this article proposes a more reasonable assumption,that random effects of each individual are independent.therefore,this article establishes the individual random effects model,it has advantage that is more flexible than the fixed effect model and the random effect model,and it can analyze whether the individual affects the overall in practical applications.In addition,this paper proposes an improved method for the mixed effect model,that obtains an improved model by nonsingular matrix factorization,and finds that the result of the score function on the score test is alawys same when the random effect variance matrix on the parameters is always equal to the diagonal matrix on the parameters.Then this paper constructs the null hypothesis under independent random effects,and established the asymptotic distribution of score test statistics.Finally,by simulating the test results of the response variables under different dis-tributions,it can be found that type I error rate is stably controlled at 0.05 in small samples,and it has stronger efficiency compared with the general Lagrange multiplier test?LM test?^[4].In the case studies,through score test under independent random ef-fects,this article obtain the individual differences of salamanders?amphibians?at different periods,and the discrepancy of the district on the consumption.