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I am performing model selection using the anova() function in R. Model 1 is a 'baseline' model involving an interaction of the experimental manipulandum as the predictors. Each subsequent model involves the addition of a time-invariant predictor (i.e. some participant characteristics that were measured but not manipulated) as a main-effect covariate to the previous model. Thus, to my understanding, each model is nested within the subsequent model. The output is as follows:

Model df      AIC      BIC    logLik   Test  L.Ratio p-value
    1 11 1319.522 1353.349 -648.7610                        
    2 12 1320.547 1357.450 -648.2737 1 vs 2 0.974570  0.3235
    3 13 1314.144 1354.121 -644.0720 2 vs 3 8.403558  0.0037
    4 14 1314.880 1357.932 -643.4398 3 vs 4 1.264430  0.2608
    5 15 1316.872 1363.000 -643.4361 4 vs 5 0.007398  0.9315
    6 16 1318.314 1367.517 -643.1569 5 vs 6 0.558260  0.4550
    7 17 1320.067 1372.345 -643.0334 6 vs 7 0.247131  0.6191

According to the p-values in the final column the addition of the new predictor in model 3 delivers the only significant improvement in model fit over the baseline model.

My question is what tests does the anova() function perform by default to arrive at the p-value for each test? Is it chi-squared based on change in residual sums of squares, or is it based in some way on log-Likelihood/ Information Criteria/Deviance statistics? The help page for this function doesn't give a lot of detail about the method used to derive this p-value and as far as I can tell there are a lot of different ways to compare models.

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  • $\begingroup$ The 'L. Ratio' means 'likelihood ratio' so it is the p value of a likelihood ratio test. $\endgroup$
    – user83346
    Jul 25 '16 at 4:49
  • $\begingroup$ Thank you @fcop. Do you know how the L.Ratio statistic is derived and what test is used to derive it (e.g. chi-squared)? $\endgroup$
    – llewmills
    Jul 26 '16 at 1:09
  • $\begingroup$ see this answer, under the section 'Intuition behind the likelihood ratio test': stats.stackexchange.com/questions/169524/… and this link: warnercnr.colostate.edu/~gwhite/fw663/LikelihoodRatioTests.PDF $\endgroup$
    – user83346
    Jul 26 '16 at 5:41
  • $\begingroup$ Ah so the LRatio is the 2 times the difference of the log likelihoods. Thank you so much @fcop. $\endgroup$
    – llewmills
    Jul 26 '16 at 10:17

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