CODEWITHSUNDEEP
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llewmills
llewmills

Reputation: 3568

What is the value of the log-likelihood returned by anova() function

I am performing model selection for a bunch of nested models using the anova() function in R. Each subsequent model has the addition of a single covariate to the previous model. I am wondering how the logLik column is derived. I understand that it is the natural logarithm of something (i.e. in the model below it is a very small number), but what I do not know is exactly what it is a logarithm of. Is it the maximum likelihood estimate under that model, i.e. a single value, or is it the result of the multiplication of the probabilities of numerous parameter values? Apologies, I know this is a fairly fundamental thing not to know.

Model df      AIC      BIC logLik   Test L.Ratio p.value
    1 11 1319.522 1353.349 -648.8                   
    2 12 1320.547 1357.450 -648.3 1 vs 2   0.975   0.324
    3 13 1314.144 1354.121 -644.1 2 vs 3   8.404   0.004
    4 14 1314.880 1357.932 -643.4 3 vs 4   1.264   0.261
    5 15 1316.872 1363.000 -643.4 4 vs 5   0.007   0.931
    6 16 1318.314 1367.517 -643.2 5 vs 6   0.558   0.455
    7 17 1320.067 1372.345 -643.0 6 vs 7   0.247   0.619

Upvotes: 0

Views: 1338

Answers (1)

Ben Bolker
Ben Bolker

Reputation: 226332

The numbers in the logLik column are the log-likelihoods (actually technically log-likelihood densities) of the entire data set under each model (at the maximum likelihood estimates for that model); because the individual observations are assumed to be independent, the likelihood of each model is the product of the likelihoods of the individual observations, or equivalently the log-likelihood is the sum of the log-likelihoods of the individual observations ...

Upvotes: 1

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