Guide Model Based Inference in the Life Sciences: A Primer on Evidence

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The text is written for people new to the information-theoretic approaches to statistical inference, whether graduate students, post-docs, or professionals. Readers are however expected to have a background in general statistical principles, regression analysis, and some exposure to likelihood methods. This is not an elementary text as it assumes reasonable competence in modeling and parameter estimation. The writing style is pragmatic and appropriate for someone without advanced statistical training. Readers looking to recommend a book on information-criteria-based modeling to colleagues who are not statisticians, or looking to locate such a book for their libraries are likely to be satisfied with this book.

It is focused on advocating and teaching the approach. It includes some history and philosophy with the methods, and each chapter ends with exercises. For those who are already familiar with model-based inference For those who are new to model-based inference, it provides a good conceptual and technical introduction. This monograph expounds ideas that the author has developed over many years with Burnham. It is heavily example-based, and aimed at working scientists.

Examples are predominately from ecological studies. This is an interesting and challenging Maindonald, International Statistical Review, Vol.

ISBN 13: 9780387740737

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In addition, we get unconditional estimates of the model coefficients first column. These are model-averaged parameter estimates, which are weighted averages of the model coefficients across the various models with weights equal to the model probabilities. These values are called "unconditional" as they are not conditional on any one model but they are still conditional on the models that we have fitted to these data; but not as conditional as fitting a single model and then making all inferences conditional on that one single model.

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Moreover, we get estimates of the unconditional standard errors of these model-averaged values. These standard errors take two sources of uncertainty into account: 1 uncertainty within a given model i. The model-averaged parameter estimates and the unconditional standard errors can be used for multimodel inference, that is, we can compute z-values, p-values and confidence interval bounds for each coefficient in the usual manner.

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We can also use multimodel methods for computing predicted values and corresponding confidence intervals. Again, we do not want to base our inferences on a single model, but all models in the candidate set. Doing so requires a bit more manual work, as I have not yet found a way to use the predict function from the glmulti package in combination with metafor for this purpose. So, we have to loop through all models, compute the predicted value based on each model, and then compute a weighted average using the model weights of the predicted values across all models.

Let's consider an example.

Model Based Inference in the Life Sciences: A Primer on Evidence

Suppose we want to compute the predicted value for studies with a treatment length of 15 weeks that used in-class writing, where feedback was provided, where the writing did not contain informational or personal components, but the writing did contain imaginative components, and prompts for metacognitive reflection were given:. Then we can obtain the predicted value for this combination of moderator values based on all models with:. One can of course also include models with interactions in the candidate set. However, when doing so, the number of possible models quickly explodes or even more so than when only considering main effects , especially when fitting all possible models that could be generated based on various combinations of main effects and interaction terms.

In the present example, we can figure out how many models that would be with:. Fitting all of these models would not only test our patience and would be a waste of valuable CPU cycles , it would also be a pointless exercise even fitting the models above could be critiqued by some as a mindless hunting expedition — although if one does not get too fixated on the best model, but considers all the models in the set as part of a multimodel inference approach, this critique loses some of its force.

So, I won't consider this any further in this example. The same principle can of course be applied when fitting other types of models, such as those that can be fitted with the rma. One just has to write an appropriate rma. Making this work would require a bit more work.

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Time permitting, I might write up an example illustrating this at some point in the future. One disadvantage of the glmulti package is that it requires Java to be installed on the computer so if you install and load the glmulti package and get an error that the rJava package could not be loaded, this is likely reflect this missing system requirement.

As an alternative, we can also use the MuMIn package. So, let's replicate the results we obtained above. First, we install and load the MuMIn package and then evaluate some code that generates two necessary helper functions we need so that MuMIn and metafor can interact as necessary:. Now we can fit all models and examine those models whose AICc value is no more than 2 units away from that of the best model with:.

Note that, by default, subset recalculates the weights, so they sum to 1 for the models shown. To get the same results as obtained with glmulti, I set recalc. If you compare these results to those in object top , you will see that they are same. I have removed some of the output, since this is the part we are most interested in.

These are the same results as in object mmi shown earlier. Note that, by default, model.

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To get the same results as we obtained with glmulti, I set revised. Anderson, D.

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Model based inference in the life sciences: A primer on evidence. Score function and Fisher information. EM Algorithm. Robustness of likelihood specification. Estimating equation and quasilikelihood. Empirical likelihood. Likelihood of random parameters. Random and mixed effects models. Nonparametric smoothing.

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