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Nonlinear Models

  • "Like doctors, data scientists should pledge a Hippocratic Oath, one that focuses on the possible misuses and misinterpretations of their models," is a quote by American mathemetician and data scientist Cathy O'Neil (1972 - ).  The quote is found on page 205 of her 2016 award winning book Weapons of Math Destruction.

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  • A cartoon suitable for use in teaching about model fitting techniques. The cartoon is number 2048 from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

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  • This NASA-HANDBOOK is published by the National Aeronautics and Space Administration (NASA) to provide a Bayesian foundation for framing probabilistic problems and performing inference on these problems. It is aimed at scientists and engineers and provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models. The overall approach taken in this document is to give both a broad perspective on data analysis issues and a narrow focus on the methods required to implement a comprehensive database repository.

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  • This presentation was given by Aneta Siemiginowska at the 4th International X-ray Astronomy School (2005), held at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA. 

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: partial/conditional tables, confounding, types of independence (mutual, joint, marginal, and conditional), identifiability constraints, partial odds ratios, hierarchical log-linear model, pairwise interaction log-linear model, conditional independence log-linear model, goodness of fit, and model building.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: ordinal regression models, cumulative probabilities, non-proportional odds, score stat for proportionl odds, MLEs, the adjacent categories logit, and proportional odds model.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: maximum likelihood estimation for logistic regression, sample size requirements for approximate normality of the MLE’s, confidence intervals, likelihood ratio statistic, score test statistic, deviance, Hosmer-Lemeshow goodness-of-fit statistic, the Hosmer-Lemeshow statistic, parameter estimates, scaled/unscaled estimates, residuals, grouped binomials, and model building strategies.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: iterative solutions to non-linear equations, score equations for exponential class variables, Newton-Raphson vs. Fisher’s Scoring, Logistic Regression for an R × 2 tables, saturated model, odds ratios when rows are not ordinal, goodness of fit, likelihood ratio statistic for nested models, and residuals.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: linear probability model, non-constant variance, logistic model, logit transformation, and probit link.

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  • This presentation discusses modeling cluster correlation explicitly through random effects, yielding a generalized linear mixed effects models (GLMM). Part II contains many examples of application to different studies.

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