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Econometrics. Princeton University Press).
In view of this fact, dependent linear models of their unknown parameters are more susceptible than their non-linearly related counterparts. The resulting estimators, then, become more easily determinant due to these existent statistical properties. However, this leads to another complication; the response function then implies that the outcome is binary. Though possible to estimate the simple linear regression model, the independent variable y takes on the binary values of either 0 or 1 (Hayashi, Fumio (2000). Econometrics. Princeton University Press).
But are the problems? Why are there problems?
"Well, yes. Actually, there are three particular problems that arise with binary dependent variables in linear regression models. Each of these makes the use of linear regression inappropriate and signifies the need for an alternative approach. The discussion...
Administration next provides these three reasons:
The error terms cannot be distributed normally... [so] the assumption of normally distributed errors cannot be appropriate.
The error terms do not have equal variances when the response variable is an indicator variable taking on variables of 0 and 1. The happens because the variance of Y depends on the value of X; consequently, the error variances are different for different levels of X. As a result, ordinary least squares is no longer optimal.
Finally, the response function represents the set of probabilities when the outcome variable is equal to either 0 or 1. The mean responses from the response function thus are constrained within the limits of 0 and 1, because 0
Sources:
Zhang, Yahong. Yang, Kaifeng. Citizen Participation in the Budget Process: the Effect of City Managers. J. Of Public Budgeting, Accounting, and Financial Management, 21 (2), 289-317. 2009. Web. 23 March 2011.
Tibshirani, Robert (1996). "Regression Shrinkage and Selection via the Lasso." Journal of the Royal Statistical Society. Series B (Methodological) 58 (1): 267 -- 288.
Yang, Kaifeng. Miller, Gerald J., eds.: Handbook of Research Methods in Public. Administration. Boca Raton, FL, USA, Auerbach, Taylor & Francis CRC Press. (2008) 823 -- 839
Lai, T.L.; Robbins, H; Wei, C.Z. (1978). "Strong consistency of least squares estimates in multiple regression." Proceedings of the National Academy of Sciences USA 75 (7).
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