What does it mean for a model to hold against another? I'm reading Agresti's Categorical Data Analysis, and I keep seeing the phrase "the model holds" and I'm not sure what it means. For example in chapter 4.5.4 on comparing GLMs using Deviance he says

Assuming that model $M_1$ holds, the likelihood-ratio test of the hypothesis that $M_0$ holds uses the test statistic 
  $$ -2[ L(\hat{\mu_0} ; y) - L(\hat{\mu}_1 ; y)]\\\ \dots $$

 A: I can only venture that the phrase "model holds" means something like "model is sensible/adequate/appropriate". 
When you are testing one model against another, usually you are testing these two hypotheses:
Ho: Model 1 is sensible/adequate/appropriate 
versus 
Ha: Model 2 is sensible/adequate/appropriate.
Usually, Model 2 is obtained from Model 1 via the inclusion of additional predictor terms.
A: To address Glen_b's comment:
The author of the book uses vague terminology, which I was just trying to bring some intuition to, especially since I don't know the specific form of the models being compared. 
When we are comparing competing models, we are ultimately comparing whether or not the models provide adequate representations for the phenomenon we study in the target population and we do so using the data at hand. 
We can formulate the hypotheses being tested when comparing competing models in formal terms, say like this:
Ho: beta3 = 0 
Ha: beta3 != 0 
if the "null" model did not include the predictor X3 whose coefficient is beta3 and the "alternative" model did (and that was the only difference between the two models).  
But even though the more formal hypotheses only involve beta3 in this example, they are tested under implicit conditions such as: the study was designed right, the research question is sensible, the data were collected properly and cleaned up well prior to being used for modeling, the class of models considered is appropriate for answering the research question and the nature of the data, etc. Violations of any or some of these implicit conditions will invalidate the results of the test. 
While we strive for mathematical simplicity when stating hypotheses, the reality in the trenches is that we are dealing with much more complicated situations and that we are testing more complicated things than we think we are:
Ho: beta3 = 0 + implicit conditions
Ha: beta3 != 0 + implicit conditions
This is my view and others may disagree, which is fine with me.
