Mixed model vs. n-way ANOVA for hierarchical data and proportions I have a experimental setup (plant germination). I don't have concrete data yet. I am looking at how many plants germinate in given conditions, broken down as follows:
1) Two different temperatures.
2) For each of the two temperatures, I have 4 salinity concentrations.
3) For each salinity concentrations I have 2 levels of habitat from which the seeds were collected.
4) For each habitat type I have specific locations from which the seeds were collected.
The measure of interest (response) is the proportion of seeds that germinated at various time intervals. I know some people approached this via n-way ANOVA (judging from the literature). But it seems to be that a mixed model may be (more) appropriate.
QUESTIONS:
1) What would be a better approach and why?
2) If one used a mixed model, which of the variables (location, habitat type, salinity) would you include as a random effect?
3) Given that these are proportion or percentage data, what would be the best approach?
 A: 
1) What would be a better approach and why?

(General) linear mixed models are much more flexible in modeling your data. For example, as you already mentioned you have to identify random terms. Random terms are variables for which you want variances to be estimated, i.e. you are not interested in mean values but more interested in capturing and accounting for the variation between those groups in your analysis. Furthermore, you would also add those variables in the random statement on which you performed multiple measurements, for example Subjects in a repeated-measures design. Here's more to read for you regarding this question:


*

*Diagnostics for generalized linear (mixed) models (specifically residuals)

*What is the difference between fixed effect, random effect and mixed effect models?

2) If one used a mixed model, which of the variables (location, habitat type, salinity) would you include as a random effect?

Since there are multiple levels of nesting in your design (hierarchical design), this should go in the random statement. However, identifying the exact nature of the nesting structure depends on the statistical software you use and how your variables are set up. There are many posts here on CrossValidated on how to do this. For example: Mixed Effects Model with Nesting

3) Given that these are proportion or percentage data, what would be the best approach?

If you are using germination success (yes/no) as an outcome and want to have random effects calculated, I would go with a general linear mixed effects model and specify the binary nature of your outcome in the model. For example see here:


*

*Fitting a binomial GLMM (glmer) to a response variable that is a proportion or fraction

*How to apply binomial GLMM (glmer) to percentages rather than yes-no counts?
And in case you are using R, have a look here too:
http://glmm.wikidot.com/faq#toc27
