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Logistic Regression A Self Learning Text

Classical categorical regression models such as the multinomial logit and proportional odds models are shown to be readily handled by the vector generalized linear and additive model (VGLM/VGAM) framework. Additionally, there are natural extensions, such as reduced-rank VGLMs for dimension reduction, and allowing covariates that have values specific to each linear/additive predictor, e.g., for consumer choice modeling. This article describes some of the framework behind the VGAM R package, its usage and implementation details.

The VGAM Package for Categorical Data Analysis

Logistic regression (LR), discriminant analysis (DA), and neural networks (NN) were used to predict ordered and disordered regions in proteins. Training data were from a set of non-redundant X-ray crystal structures, with the data being partitioned into N-terminal, C-terminal and internal (I) regions. The DA and LR methods gave almost identical 5-cross validation accuracies that averaged to the following values: 75.9 +/- 3.1% (N-regions), 70.7 +/- 1.5% (I-regions), and 74.6 +/- 4.4% (C-regions). NN predictions gave slightly higher scores: 78.8 +/- 1.2% (N-regions), 72.5 +/- 1.2% (I-regions), and 75.3 +/- 3.3% (C-regions). Predictions improved with length of the disordered regions. Averaged over the three methods, values ranged from 52% to 78% for length = 9-14 to >/= 21, respectively, for I-regions, from 72% to 81% for length = 5 to 12-15, respectively, for N-regions, and from 70% to 80% for length = 5 to 12-15, respectively, for C-regions. These data support the hypothesis that disorder is encoded by the amino acid sequence.

Predicting Protein Disorder for N-, C-, and Internal Regions.

When a study outcome is rare in all strata used for an analysis, the odds ratio estimate of causal effects will approximate the risk ratio; therefore, odds ratios from most case-control studies can be interpreted as risk ratios. However, if a study outcome is common, the odds ratio will be further from 1 than the risk ratio. There is debate regarding the merits of risk ratios compared with odds ratios for the analysis of trials and cohort and cross-sectional studies with common outcomes. Odds ratios are conveniently symmetrical with regard to the outcome definition; the odds ratio for outcome Y is the inverse of the odds ratio for the outcome not Y. Risk ratios lack this symmetry, so it may be necessary to present 1 risk ratio for outcome Y and another for outcome not Y. Risk ratios, but not odds ratios, have a mathematical property called collapsibility; this means that the size of the risk ratio will not change if adjustment is made for a variable that is not a confounder. Because of collapsibility, the risk ratio, assuming no confounding, has a useful interpretation as the ratio change in average risk due to exposure among the exposed. Because odds ratios are not collapsible, they usually lack any interpretation either as the change in average odds or the average change in odds (the average odds ratio).

https://jamanetwork.com/journals/jamapediatrics/articlepdf/381459/pra80010_438_445.pdf

The relative merits of risk ratios and odds ratios.

Introduction.- Basic Reliability Theory.- Stochastic Failure Models.- Availability Analysis of Complex Systems.- Maintenance Optimization.

Stochastic Models in Reliability

The Tools of Statistical Inference. Distribution Theory for Count Data. Binary Contingency Tables. Binomial Regression Models. Smoothing Binomial Data. Poisson Regression Models. Conditional Inference. Index.

Statistical Analysis of Categorical Data

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Statistical Analysis of Categorical Data