# Mixed Effects Models

## lmers and glmers

I got reviewer comments back on my Manchester paper! One of the reviewers suggested I used linear mixed effect models instead of a binomial GLM to evaluate gonad maturity before and after treatment. They also suggested I use a linear mixed effect model instead of a one-way ANOVA to look at differences in D-hinge count too. By using such a model, I can account for random effects, like experimental tank or sire.

To create a linear mixed model in R, I needed the `lme4`

package. Within the package, I can use `lmer`

for a linear mixed model and `glmer`

for a generalized linear mixed model. The syntax is the same as `lm`

or `glm`

, but I can add random effects with the following term:

y ~ x + (1 RANDOM-VARIABLE)

### Gonad maturation

After talking to Tim and reviewing this guide, I tackled a generalized linear mixed effect model for gonad maturation differences before and after treatment. In my data sheet, I added a column for tank. Pre-treatment oysters were all in the same tank, “Pre,” and post-treatment oysters were coded based on their experimental tank. This is when I ran into a problem. Remember how my tissues got mixed up during processing so I had a bunch of unknown tissues from the ambient treatment? I added all of those to the same “unknown tank.” While they didn’t mix up any treatments, I actually have no way of tracing back the experimental tank for all but two of my ambient treatment tissues. If I cannot assign a tank to these tissues, a `glmer`

that uses tank as a random effect may not be appropriate. I went through with the analysis in this R script, I emailed Tim with my concerns and will update the code as necessary.

### D-hinge counts

I did something similar for my D-hinge counts. Instead of a `glmer`

, I used a `lmer`

. First, I specified the sire in a column in this spreadsheet. I used a `lmer`

in this R script and found that the variance for the random effect overlapped zero. This means that the random effect probably doesn’t have much weight, and I can 1) pool by male treatment and 2) use a normal linear model or ANOVA. When looking at the `lmer`

, I had an chi-squared p-value of 0.02445, meaning there were significant differences between all four treatments. I would need to unpack this more to figure out which pairwise differences were significant. I also used a `lmer`

when pooling male treatments, and found that once again, the variance for the random effect (sire) overlapped zero. My ANOVA p-value was 0.00271.

Now that I understand how to use `lmer`

and `glmer`

, I need to understand how to interpret my results. I think a little more reading will help me with this.

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