How to select (and nest) covariates in a crossed design model?

Thank you for the quick reply. First, I?ll try to explain my experiment more clearly. The study was done in two separate, enclosed areas, which were of the same size and fairly similar in their environment and animal density. I would still like to account for their differences by including the area as a covariate (because I know there were some differences between them that simply could not be helped). Three session levels were assigned, aiming to control for pre-experiment differences between enclosures (before) and to measure the immediate (during) and later response (after) to the treatment. During each session, both of the enclosed study areas were measured once per day, three days in a row, to have three observations of each session. Animal densities within areas were monitored, and the response variables were then scaled according to those densities. The experiment was repeated with reversed treatments, with precisely the same time intervals as the first experiment.

(1) Experiments 1 and 2 were identically replicated, having the same sessions (though done at two consequent periods) and number of observations. Only the treatments were reversed to reduce the impact of areas.

Study units are the areas A and B, where a compiled response was measured (from 50 separate, evenly distributed points, and then summed up), and scaled by the density of animals present in the enclosed area. So observations of areas A and B were always conducted on the same day (= on the same round), thus forming a pair.

(2) I have a day-variable on my data, but I think using e.g. session number (from 1-6, sessions 1-3 repeated twice) would be a useful time variable. Also rounds (1-18) act as a time variable, representing the days when actual measurements were taken (omitting those days in between).

(3) ?Before? - session level (including three observation, as do all sessions) was measured four times: in both areas during both experiments. The role of this session level was indeed to represent a baseline measure, and to see how comparable the two areas were to begin with. Related to question (4), it was also useful when estimating whether time lag between the switching of regimes was sufficient.

I?ve considered nesting the session numbers within experiments (experiment 1 & session 1-3, experiment 2 & sessions 3-6), but my problem is that sessions are conducted precisely in the same way in both experiment times (?before?, ?during? and ?after? x2). Also, is it a problem to use two interrelated factors, one as fixed and one as random? Or possibly even the same variable ("session") in both categories at the same time?

As said, round observations would be useful mainly to quantify measurement error within session. Perhaps then I should simplify my data table and use round-means as a session observation, instead of using 3 separate round values?

I decided to use generalized linear mixed model, because the response variable is not normally distributed, but requires a log link function. The study is also supposed to include similar data from following year, but I had some problems with the experimental set up, so I'm currently looking at only one year. I hope this information helps with the obscurity and makes it easier to evaluate, which kind of model would fit my data, or whether the data contains too few repetitions to be properly analysed at all.

  - Mari -

----- Original Message -----
From: Dennis Murphy <djmuser at gmail.com>
Date: Friday, July 15, 2011 2:23 pm
Subject: Re: [R-sig-ME] How to select (and nest) covariates in a crossed design model?
To: Mari Laine <mslain at utu.fi>
Cc: r-sig-mixed-models at r-project.org

How to select (and nest) covariates in a crossed design model?

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