# Using DIC to test which data should be used - different sample sizes

I have a glmm model

$y \sim b_1 * b_2 * b_3 + random$

where $b_i$ are the fixed effects. I am using DIC to compare models and select the best fitting model. I also have some options in setting up my model. For example, $b_1$ is the average spring temperature in the individuals first 5 years of life. This can be calculated in two ways:

Approach 1 - stringent:

Average temperature is calculated only in cases where all five years have data, such that if an individual was born in the year $x_0$, we would need information on temperature for years $x_0$ through $x_4$ to get the 5 year average.

Approach 2 - relaxed:

Average temperature is calculated for all cases where at least one of the 5 years has data recorded. Therefore, if we had the temperature for years $x_0$, $x_1$ and $x_4$ the score for $x_0$ individuals would be $\frac{(x_0 + x_1 + x_4)}{3}$, and for $x_1$ individuals $\frac{(x_1 + x_4)}{2}$ etc..

Can I use DIC based model selection to choose approach? The random effects and all other model structure is the same, it's just a case of substituting fixed effect $b_1$. Because the data is more stringently selected in approach 1 it greatly reduces the sample size, but it does mean the samples are more precise: does the different sample size in either model have impacts on my decision to use DIC based model selection methods?

Judging from the answer on my previous question I suspect the answer is that I can make this comparison. However, it would be really excellent to get a citable source on this.

As another illustration, imagine I have data from two populations, with measures taken over many years. Greater sampling effort was given to one population, such that there is a tendency that one population has a smaller sample size, and even has no samples some years. Could I compare models using both populations and just the well sampled data to see if the poor balance in experimental design is affecting model fit? Could I select the model with data only from the well sampled population on this basis? Does experimental balance affect DIC?