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For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally across all areas represented by the ones in your study is constant constant (i.e., it does not depend on any of your predictor variables). It doesn't appear you are interested in modelling the expected tally across all these areas given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

In contrast, the model.nb.null.off is postulating that the expected tally per squared kilometre of area is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre of area depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.

The choice of which null model to use depends on what you want to model - modeling the expected tally across all areas represented by the ones in your study requires the use of model.nb.null, whereas modeling the expected tally per squared kilometre of area requires the use model.nb.null.off.

For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally across all areas is constant. It doesn't appear you are interested in modelling the expected tally across all areas given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

In contrast, the model.nb.null.off is postulating that the expected tally per squared kilometre of area is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre of area depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.

The choice of which null model to use depends on what you want to model - modeling the expected tally across all areas requires the use of model.nb.null, whereas modeling the expected tally per squared kilometre of area requires the use model.nb.null.off.

For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally across all areas represented by the ones in your study is constant constant (i.e., it does not depend on any of your predictor variables). It doesn't appear you are interested in modelling the expected tally across all these areas given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

In contrast, the model.nb.null.off is postulating that the expected tally per squared kilometre of area is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre of area depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.

The choice of which null model to use depends on what you want to model - modeling the expected tally across all areas represented by the ones in your study requires the use of model.nb.null, whereas modeling the expected tally per squared kilometre of area requires the use model.nb.null.off.

2 added 242 characters in body
source | link

For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally across all areas is constant. It doesn't appear you are interested in modelling the expected tally across all areas given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

YourIn contrast, the model.nb.null.off is essentially postulating that the expected tally per squared kilometre of area is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre of area depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.

The choice of which null model to use depends on what you want to model - modeling the expected tally across all areas requires the use of model.nb.null, whereas modeling the expected tally per squared kilometre of area requires the use model.nb.null.off.

For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally is constant. It doesn't appear you are interested in modelling the expected tally given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

Your model.nb.null.off is essentially postulating that the expected tally per squared kilometre is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.

For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally across all areas is constant. It doesn't appear you are interested in modelling the expected tally across all areas given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

In contrast, the model.nb.null.off is postulating that the expected tally per squared kilometre of area is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre of area depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.

The choice of which null model to use depends on what you want to model - modeling the expected tally across all areas requires the use of model.nb.null, whereas modeling the expected tally per squared kilometre of area requires the use model.nb.null.off.

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For the purpose of this answer, let's say your areas are measured in squared kilometres.

Your model.nb.null is postulating that the expected tally is constant. It doesn't appear you are interested in modelling the expected tally given that tallies are compiled over areas of different magnitudes, so this model should not be a consideration for your model building procedure.

Your model.nb.null.off is essentially postulating that the expected tally per squared kilometre is constant (i.e., it does not depend on any of your predictor variables).

Since you want to investigate whether the expected tally per squared kilometre depends on any of your predictor variables, it makes sense to use model.nb.null.off as your null model and track what happens with the null model deviance as you add predictors to this null model.