Fixed parameters and default settings

[ehileman]

Hi all,

I am hoping someone can help me with the following seemingly simple question. When building reduced models that originate from a design matrix constructed global model with fixed parameters, I noticed that MARK's default setting is to retain these fixed values within the 'Fix Parameters' radio button. My question is this: should the fixed parameters values be manually removed prior to running the reduced models if the reduced models do not explicitly include the parameters that were fixed?

For example, consider the following closed capture model: N(sex), p(sex*time) = c (sex*time), where the terminal p and c for males is fixed to zero because males were not encountered in the last sampling occasion (and the last interaction term is deleted so that the number of estimable parameters is correctly reported). From this the following reduced model, N(sex), p(sex) = c(sex), is built. Should the zeros from the terminal p and c that were included with the global model, N(sex), p(sex*time) = c (sex*time), be manually removed prior to running this reduced model?

I noticed that including fixed values in such reduced models can substantially affect their real and derived estimates as well as increase their model ranking (even when the number of estimable parameters is unchanged by including the fixed parameters--like in the above reduced model example) based on deviance, AICc, weight, etc when compared to identical model without fixed parameters.

Many thanks!

Eric

[abreton]

should the fixed parameter values be manually removed prior to running the reduced models if the reduced models do not explicitly include the parameters that were fixed?

By 'manually remove' I suspect you mean remove the fixed value? The only way to actually 'remove' one of the real parameters is to modify the data/reimport into MARK. You can, in contrast, constrain reals to be the same value by reducing models, e.g., including/excluding time variation.

'Manually removing' is not possible from within MARKs design matrix ... this would be equivalent to deleting rows. The only way to 'manually remove' rows in the design matrix is to modify the PIMs. With this in mind, you could specify different sets of PIMs within a model set ... recall the PIMs dictate how many rows you'll have in the design matrix. However, in general, (intermediate mark workshop, CSU) you're advised to set your PIM structure at the start of your analysis, close the PIM windows at this point, and then proceed with ALL other model building in the design matrix. Despite being possible, having a variety of PIM structures in the same analysis would likely cause even more confusion than you're dealing with now (hence the advice to set the PIMs just one time). Also, I suspect you'd run into trouble when you tried to 'model average' across models that had different underlying PIM structures.

Regarding fixing a parameter, my advice would be to fix parameters only when it makes sense to do so. Ideally, let the software (mark in this case) estimate all parameters that are (based on the model structure) estimable. Subsequently, if you have one top model then you don't need to worry about some of the concerns that you raised. Otherwise, if model averaging is necessary, then you should not report estimates that were fixed in some models and not in others. The model averaged value will be some average (based on model weights) of the fixed and estimated real parameter ... likely a bogus estimate? The same is true for a (confounded) terminal parameter,

Consider this example,
phi(t) p(t)
phi(.) p(.)

CJS models ... one with full time ... one constant ... let's say each had a weight of 0.50 ... in this case you wouldn't want to report the model averaged terminal phi and terminal p parameters ... since these would include bogus (non-estimable) estimates from the phi (t) p (t) model.

I noticed that including fixed values in such reduced models can substantially affect their real and derived estimates as well as increase their model ranking (even when the number of estimable parameters is unchanged by including the fixed parameters--like in the above reduced model example) based on deviance, AICc, weight, etc when compared to identical model without fixed parameters.

Absolutely. Recall that estimates from a model in mark are 'maximum likelihood estimates' ... i.e., estimates of the parameters that are most likely given the data AND the model. Also note, the 'most likely' estimates reported are those that align with the 'maximum' negative point along the (often multidimensional) likelihood function representing the model. So, when you 'fix' a real parameter, you are modifying the model -- that's the first reason why the estimates you mentioned may have changed -- ... and because all estimates are based on the maximum negative point along the likelihood function (second reason) fixing one or more will affect the estimates of those that remain.

andre