Likelihood Ratio Tests

likelihood ratio tests

used to evaluate whether a more complex model is justified over a simpler one

null hypothesis of LRTs

the two models are equally effective at explaining the variation

alternative hypothesis of LRTs

the complex model does a better job at explaining the variation

LRT statistic

2 x difference of log-likelihoods

when to reject the null hypothesis of LRTs

if the LRT statistic is so large it leaves less than 0.05 to the right of it

Akaike's Information Criterion (AIC)

-2(log-likelihood) +2(number of parameters)

analysis of AICs

the lower the AIC score, the better the model fits, models within 2 AIC units are not regarded as distinguishable

Student's t-statistic

coefficient/standard error of coefficient

confidence intervals

95% of the intervals should contain the sample mean

post-hoc tests

conducted when you want to know not only whether a factor variable is significant but exactly which levels of the variable are significantly different

R-squared

the proportion of the total variation explained by the explanatory variables

when R-squared is used

when response is normally distributed and models fitted using least squares

pseudo-R-squared

equivalent of using R-squared when using maximum likelihood

pseudo-R-squared formula

null deviance - residual deviance / null deviance * 100

when to use AIC over LRTs

when you want to compare non-nested models