Purposeful selection of variables in logistic regression

Background  

The main problem in many model-building situations is to choose from a large set of covariates those that should be included in the "best" model. A decision to keep a variable in the model might be based on the clinical or statistical significance. There are several variable selection algorithms in existence. Those methods are mechanical and as such carry some limitations. Hosmer and Lemeshow describe a purposeful selection of covariates within which an analyst makes a variable selection decision at each step of the modeling process.     

Augmented Backward Elimination: A Pragmatic and Purposeful Way to Develop Statistical Models

Statistical models are simple mathematical rules derived from empirical data describing the association between an outcome and several explanatory variables. In a typical modeling situation statistical analysis often involves a large number of potential explanatory variables and frequently only partial subject-matter knowledge is available. Therefore, selecting the most suitable variables for a model in an objective and practical manner is usually a non-trivial task. We briefly revisit the purposeful variable selection procedure suggested by Hosmer and Lemeshow which combines significance and change-in-estimate criteria for variable selection and critically discuss the change-in-estimate criterion. We show that using a significance-based threshold for the change-in-estimate criterion reduces to a simple significance-based selection of variables, as if the change-in-estimate criterion is not considered at all. Various extensions to the purposeful variable selection procedure are suggested. We propose to use backward elimination augmented with a standardized change-in-estimate criterion on the quantity of interest usually reported and interpreted in a model for variable selection. Augmented backward elimination has been implemented in a SAS macro for linear, logistic and Cox proportional hazards regression. The algorithm and its implementation were evaluated by means of a simulation study. Augmented backward elimination tends to select larger models than backward elimination and approximates the unselected model up to negligible differences in point estimates of the regression coefficients. On average, regression coefficients obtained after applying augmented backward elimination were less biased relative to the coefficients of correctly specified models than after backward elimination. In summary, we propose augmented backward elimination as a reproducible variable selection algorithm that gives the analyst more flexibility in adopting model selection to a specific statistical modeling situation.     

Purposeful patterns of spontaneous calcium transients in embryonic spinal neurons

Embryonic cultured Xenopus spinal neurons generate two types of spontaneous elevation of intracellular calcium that encode developmental information in the frequency with which they are produced. Calcium spikes regulate the appearance of GABA and maturation of potassium current. Calcium waves in growth cones regulate neurite extension. Spikes and waves are also observed in neurons differentiating in situ. Because differentiation is dependent on the frequency of calcium transients, neurons that are coactive and fire spikes in concert would be expected to differentiate together. Consistent with this prediction, segmentally arrayed clusters of putative motoneurons on the ventral aspect of the neural tube fire together during development.     

Can Concurrent Speed and Directness of Travel Indicate Purposeful Encounter in the Yellow Baboons (Papio hamadryas cynocephalus) of Ruaha National Park,Tanzania?

I used components of baboon foraging behavior (concurrent fast and direct travel) to categorize core dry-season foods as purposefully or randomly encountered. I then compared the categorized foods to published, a priori predictions for core dry-season foods. Using focal-animal techniques on 6 males from two baboon troops, I collected precise locational data with a differentially corrected Global Positioning System (GPS) over 6 mo. The data analysis yielded the speed and directness of baboon travel between a food-handling event and a prior location. To distinguish purposefully encountered foods from randomly encountered foods, I calculated the average speed and the average observed deviation from straight-line travel exhibited to each resource type. A linear regression describes the relationship between these variables for each resource type. Baboons demonstrate both relatively high speeds and direct travel towards 3 food types: Combretum obovatum, impala, and baobab trees. Baboons were hypothesized a priori to encounter these resources purposefully. Baboons were also hypothesized a priori to encounter corms and perhaps Commiphora paniculatum purposefully, however, they travel neither quickly nor directly to these resources. I interpret this finding in terms of the costs accrued by traveling quickly and directly to fall-back resources. I discuss the ability of concurrent speed and directness to distinguish purposefully encountered foods from randomly encountered foods.