Best practice MLR vs GLM(M)

Question

I am modelling timeseries of organism traits (7 different traits in total) using GLM(M)s in R. The data was collected at very irregular intervals and from 6 different locations. For every location 5-10 animals were sampled and some locations have been sampled multiple times whereas others just once or twice. I am interested to see if Trait significantly changes with Year.

I decided to use Location as a random variable so that the model is of the form:

glmer(Trait~ Year + Var1 + (1|Location), 
               family=gaussian(link = "log"),
               data = data)

The model diagnostics lock good and don't give any reasons for concerns to me.

I did just for the sake of it model the same traits using multiple linear regression, this time having Location as a fixed term. This required the log transformation of Traits

lm(log(Trait) ~ Year + Var1 + Location, data = data)

Also for these models the diagnostics look good. Both models suggest the same trend in the data.

Now the problem that I am facing is decide what model I should use? In the literature it is commonly mentioned that the simplest possible statistical tool should be favored over more complicated ones which suggests to me I should favor the linear regression but one is also discouraged to transform data to fit the model.

Note that there is a difference between a model with a transformed response & with a link function for the mean (see: [Why is GLM different than an LM with transformed variable](https://stats.stackexchange.com/q/122103/7290)). These can't both be right. — gung - Reinstate Monica, Oct 14 '20 at 18:32
@gung-ReinstateMonica is quite right. I have updated my answer. You need to be consistent in what you are modelling. — Robert Long, Oct 14 '20 at 18:52

Robert Long · Accepted Answer · 2020-10-14T18:51:43.813

7

6 is considered to be at or very near the lower limit for fitting random intercepts. In your case I would suggest the linear model with fixed effects for location. If this is for publication / presentation then I would also mention that you have fitted a mixed model with random intercepts for location, and found that the inferences were very similar.

Also, note that, to be consisent, you should fit the models:

glm(Trait ~ Year + Var1 + Location, family = gaussian(link = "log"), data = data)

and

glmer(Trait ~ Year + Var1 + (1|Location),family = gaussian(link = "log"), data = data)

OR,

lm(log(Trait) ~ Year + Var1 + Location, data = data)

and

lmer(log(Trait) ~ Year + Var1 + (1|Location), data = data)

edited Oct 14 '20 at 18:51

answered Oct 14 '20 at 17:24

Robert Long

53,316
10
84
148

1

Thank you very much! This answer is great. – Globoquadrina Oct 15 '20 at 08:02
You're welcome. Happy to help ! – Robert Long Oct 15 '20 at 08:03

Best practice MLR vs GLM(M)

1 Answers1