Probit Regression and Response Models (Statistical Associates Blue Book Series 38)
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Probit Regression and Response Models (Statistical Associates Blue Book Series 38)
Probit regression is method of working with categorical dependent variables whose underlying distribution is assumed to be normal. That is, the assumptions of probit regression are consistent with having a dichotomous dependent variable whose distribution is assumed to be a proxy for a true underlying continuous normal distribution. Probit regression has been extended to cover multinomial dependent variables (more than two nominal categories) and to cover ordinal categorical dependent variables.
Probit regression is an umbrella term meaning different things in different contexts, though the common denominator is treating categorical dependent variables assumed to have an underlying normal distribution. This volume discusses ordinal probit regression, probit signal-response models, probit response models, and multilevel probit regression.
Table of Contents Introduction7 Overview7 Ordinal probit regression7 Probit signal-response models7 Probit response models8 Multilevel probit regression8 Key concepts and terms9 Probit transformations9 The cumulative normal distribution9 Probit coefficients10 Elasticity10 Significance testing11 Frequently asked questions11 What about probit in Stata?11 Binary and ordinal probit regression13 Binary and ordinal probit regression models13 Binary probit regression in generalized linear models13 Example13 Overview13 Binary probit regression output in SPSS GZLM22 Ordinal probit regression in generalized linear models28 Overview28 Example28 SPSS set-up28 SPSS ordinal probit output30 Ordinal regression with a probit link33 Overview33 SPSS set-up33 Output for ordinal regression with a probit link36 Model fitting information, goodness-of-fit, and pseudo R-square tables36 Test of parallel lines37 Parameter estimates table38 Probit signal-response models39 Overview39 Type of model40 Equal variance vs. unequal variance signal-response models41 The detection parameter, d44 Model fit45 Location-scale models47 Unequal variances model in SPSS48 Probit Response Models49 Overview49 Key concepts and terms50 Data setup51 Models52 Variables53 Unit of analysis53 Response frequency variable54 Total observations variable54 Factor54 Covariate(s)55 Weighting variable55 Example56 Example summary56 Options56 Outputs: Pearson goodness-of-fit chi-square58 Outputs: Parallelism test59 Outputs: Transformed response plots59 Outputs: Parameter estimates60 Outputs: Natural response rate61 Outputs: Cell counts and residuals62 Outputs: Confidence limits62 Outputs: Relative median potency (RMP)64 Assumptions for probit response models65 Variance in the response variable65 Parallelism.65 Linearity in the probit66 Normal distribution66 Stimulus-response.66 Conditional potencies66 Independent observations67 Adequate number of groups67 No negative counts67 Total >= response67 Frequently asked questions for probit response models68 What is the data set-up for a probit response model?68 What happens if I enter individual rather than grouped data into the Probit procedure in SPSS?68 What is the SPSS syntax for the probit response model?69 Couldn't we use OLS regression to create a response model?69 Couldn't we use a t-test instead of probit?69 Multilevel probit regression70 Overview70 Example70 Sample size in GLMM70 SPSS multilevel probit set-up71 Defining the subject structure of the data71 The "Fields & Effects" tab72 The "Build Options" tab75 The "Model Options" tab76 SPSS multilevel probit output77 Model viewer77 The "Model Summary" table79 The "Data Structure" table80 Predicted by Observed" plot80 The "Classification" table80 The "Fixed Effects" table and diagram81 The "Fixed Coefficients" table and diagram83 The "Random Effect Covariances" table85 The "Estimated Means" table88 Bibliography90 Pagecount: 92