Is it possible to use probit model in a pooled cross sectional dataset? While there are literature around application of the probit model in panel data, I wonder if there are specific examples of probit model in a pooled cross sectional dataset.
Your question is an important one! Caution is urged when applying techniques to different applications. As we think about the results of a Probit model effectively being probabilities, it is important that the results can be applied to all aspects of the sample before they can be generalized to the population.
For example, you can go to Wooldridge's Introductory Econometrics book, chapter on Limited Dependent Variable Models and Sample Selection Corrections and reproduce thes example there.
http://fmwww.bc.edu/gstat/examples/wooldridge/wooldridge17.html
An example in my own publications:
http://www.scielo.org.mx/pdf/ineco/v66n261/0185-1667-ineco-66-261-00119.pdf
There are lots of examples in transport research because of concerns about IIA , red bus, blue bus problem.
comparing logit and probit see
https://www.researchgate.net/post/How_to_decide_on_which_model_Logit_or_Probit_to_use_when_modeling_the_business_cycle_phase
And on IIA, see
https://sawtoothsoftware.com/help/lighthouse-studio/manual/hid_thered-bus.html
https://stats.stackexchange.com/questions/147489/iia-assumption-difference-logit-and-probit
I personally prefer the assumptions of dataset and model should be matched
see detail.....
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example, married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model.
A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such as an estimation being called a probit regression.
Md Azizur Rahman just adding some things : a probit does not have to be binary response; it can be a proportion in which the numerator is subset of the denominator - see my comments on the same issue in relation to the logit. https://www.researchgate.net/post/What-is-the-difference-between-linear-regression-and-logistics-regression
Indeed, the terms probit was first used by Chester Bliss 1934 article on how to analyse data such as the percentage (proportion) of a pest killed by a pesticide.
Bliss CI. (1934). "The method of probits". Science. 79 (2037): 38–39. doi:10.1126/science.79.2037.38. "These arbitrary probability units have been termed ‘probits’" (p. 39) although the idea is much older; D. J. Finney Probit Analysis 2nd edition (1952, pp. 42-6) traces the underlying principle back to Fechner and his work on psychophysics in 1860 (https://jeff560.tripod.com/p.html)
There is also no need for it two be only two values - there is such a thing as the multinomial probit with multiple categories ( Daganzo, Carlos, 1979, Multinomial Probit: The Theory and Its Application to Demand Forecasting ).
Finally there is also the multivariate probit model, which is used to model correlated binary outcomes (or proportions); Chib, S., & Greenberg, E. (1998). Analysis of Multivariate Probit Models. Biometrika, 85(2), 347-361. https://www.jstor.org/stable/2337362
For an example of the possibilities, see Article Investigating the Macro Determinants of Self-Rated Health an...
I am making these comments lest people think the approach is more limited than it is.
A probit model uses the standard normal distribution (usually with mean = 0 and variance = 1). Rather than being strictly confined merely to binary dependent variable where odds ratios are computed, a multinomial dependent variable can be used and coefficients can be estimated rather than merely odds ratios strictly in case of a binary dependent variable.
- Badges
- Science topic