An Example of a Latent Regression Model:

Nakosteen and Zimmer (1980) constructed a model of migration for  the US using  the latent regression  approach. Let  the market wage earned by  individual i,  earns at his/her present location be  

Independent  variables  in  the  equation include  age,  gender,  race,  growth  in employment, and growth  in  per capita income. If the  individual migrates to a  new location, then hisher market wage becomes

However, migration entails costs for the individual, say,

Individuals migrate if the benefit Y_P*-  Y_m*  is greater than the cost C*.  The net benefit of moving is

We do not observe M  .  We observe only that M = 1 for a move and M = 0 for no move.  If  fhe  disturbances  are  normally  distributed,  then  the  probit  model is produced. Logistic disturbances produce the logit model instead.