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
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