Probit Regression and Response Models (Statistical Associates Blue Book Series 38)

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