I am trying to determine which evolutionary model is best for my discrete data using the function fitDiscrete() from the geiger package.

These are the values that I get for the number of parameters (k), maximum log likelihood (lnL), AIC and AICc for each model:

     k   lnL        AIC       AICc
ER   1   -115.8006  233.6012  233.6637
ARD  90  -85.98459  351.9692  -303.2308
SYM  45  -97.23202  284.4640  491.464

The same dataset (n = 66), tree and single trait with 10 levels were used to create each model. The only difference is the evolutionary model fitted (equal rates (ER), all rates different (ARD) and symmetrical rates (SYM))

I am having trouble interpreting these results, however.

To start, for AIC, I'm fairly sure that I should select the model with the smallest AIC score, i.e the ER model.

For lnL, however, I have seen that the model with the "largest value" should be selected with this being interpreted as the value closest to 0 (https://www.r-phylo.org/wiki/HowTo/Ancestral_State_Reconstruction), i.e. the ARD model. I realise though that lnL values tend to be biased towards models with higher k values. To address this, I did do a likelihood test as suggested by the website above (chi-squared test), which came to p < 0.001. This would suggest that the ARD model should be preferred over the ER model, which contradicts what the AIC scores are telling me.

As for AICc, again, the "smallest value" should be selected but the negative sign mixed in with the positive ones has thrown me. Is this the smallest absolute value or the value value closest to negative infinity?

So, all in all, how can I tell which model should be preferred?

Thanks,

Carolina

I am trying to determine which evolutionary model is best for my discrete data using the function fitDiscrete() from the geiger package.

These are the values that I get for the number of parameters (k), maximum log likelihood (lnL), AIC and AICc for each model:

     k   lnL        AIC       AICc
ER   1   -115.8006  233.6012  233.6637
ARD  90  -85.98459  351.9692  -303.2308
SYM  45  -97.23202  284.4640  491.464

The same dataset (n = 66), tree and single trait with 10 levels were used to create each model. The only difference is the evolutionary model fitted (equal rates (ER), all rates different (ARD) and symmetrical rates (SYM))

I am having trouble interpreting these results, however.

To start, for AIC, I'm fairly sure that I should select the model with the smallest AIC score, i.e the ER model.

For lnL, however, I have seen that the model with the "largest value" should be selected with this being interpreted as the value closest to 0 (https://www.r-phylo.org/wiki/HowTo/Ancestral_State_Reconstruction), i.e. the ARD model. I realise though that lnL values tend to be biased towards models with higher k values. To address this, I did do a likelihood test as suggested by the website above (chi-squared test), which came to p < 0.001. This would suggest that the ARD model should be preferred over the ER model, which contradicts what the AIC scores are telling me.

As for AICc, again, the "smallest value" should be selected but the negative sign mixed in with the positive ones has thrown me. Is this the smallest absolute value or the value value closest to negative infinity?

So, all in all, how can I tell which model should be preferred?