Modelling Binary Data, Second EditionSome examples; The scope of this book; Use of statistical software; Further reading; Statistical inference for binary data; The binomial distribution; Inference about the success probability; Comparison of two proportions; Comparison of two or more proportions further reading; Models for binary and binomial data; Statistical modelling; Linear models; Methods of estimation; Fitting linear models to binomial data; Models for binomial response data; The linear logistic model; Fitting the linear logistic model to binomial data; Goodness of fit a linear logistic model; Comparing linear logistic models; Linear trends in proportions; Comparing stimulus-responses relationships; Non-convergence and overfitting; A further example on model selection; Predicting a binary response probability further reading; Bioassay and some other applications; The tolerance distribution; Estimating and effective dose; Relative potency; Natural response; Non-linear logistic regression models; Applications of the complementary log-log model further reading; Model checking; Definition of residuals; Checking the form of the linear predictor; Checking the adequacy of the link function; Identification of outlying observations; Identification of influential observations; Checking the assumption of a binomial distribution; Model checking for binary data; Summary and recommendations; A further example on the use of diagnostics further reading; Overdispersion; Potential causes of overdispersion; Modelling variability in response probabilities; Modelling correlation between binary responses; Modelling overdispersed data; The special case of equal ni; The beta-binomial model; Random effects in a linear logistic model; Comparison of methods; A further example on modelling overdispersion; Modelling data from epidemiological studies; Basic designs for aetiological studies; Measures of association between disease and exposure; Confounding and interaction; The linear logistic model for data from cohort studies; Interpreting the parameters in a linear logistic model; The linear logistic model for data from case-control studies; Matched case-control studies; A matched case-control study on sudden infant death syndrome; Some additional topics; Analysis of proportions and percentages; Analysis of rates; Analysis of binary data from cross-over trials; Random effects modelling; Modelling errors in the measurement of explanatory variables; Analysis of binary time series; Multivariate binary series; Experimental design; Computer software for modelling binary data; Statistical packages for modelling binary data; Computer-based analyses of example data sets; Using packages to perform some non-standard analyses; Summary of the relative merits of packages for modelling binary data. |
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approximate B₁ binary data binary observations binomial distribution BMDP case-control study change in deviance chol confidence interval confounding variables constructed variable corresponding data from Example data set degrees of freedom density deviance on fitting diverticular disease ED50 value EGRET equation explanatory variables exposure factor fitted model fitted probabilities fitted values fitting a linear fitting the model full model Genstat germination index plot indicator variables individual interaction ith observation likelihood function likelihood residuals linear logistic model link function log acid logistic regression lines logistic regression model logistic transform matched set matrix mean deviance method model fitted model that contains nodal involvement obtained odds ratio outliers overdispersion P-value p₁ package parameter estimates particular probit proc probit procedure random effect random variable response probability response variable rotifers species ẞo standard error standardized deviance residuals statistic success probability variance variance-covariance matrix x²-distribution zero