Probit functions effect models

In the panel data models estimated in Example 21.5.1, neither the logit nor the probit model provides a framework for applying a Hausman test to determine whether fixed or random effects is preferred. Explain. (Hint Unlike our application in the linear model, the incidental parameters problem persists here.) Look at the two cases. Neither case has an estimator which is consistent in both cases. In both cases, the unconditional fixed effects effects estimator is inconsistent, so the rest of the analysis falls apart. This is the incidental parameters problem at work. Note that the fixed effects estimator is inconsistent because in both models, the estimator of the constant terms is a function of 1/T. Certainly in both cases, if the fixed effects model is appropriate, then the random effects estimator is inconsistent, whereas if the random effects model is appropriate, the maximum likelihood random effects estimator is both consistent and efficient. Thus, in this instance, the random effects satisfies the requirements of the test. In fact, there does exist a consistent estimator for the logit model with fixed effects - see the text. However, this estimator must be based on a restricted sample observations with the sum of the ys equal to zero or T muust be discarded, so the mechanics of the Hausman test are problematic. This does not fall into the template of computations for the Hausman test. 

For the Excel spreadsheets, a number of the effect models use probit equations. The conversion from probit to percentage is accomplished, in some examples, using the ERF function. This function is only avalable to Excel if the analysis tookpack is loaded. 

This allows the calculation of an effect expected according to the concept of response addition for any concentration of the mixture. Again, the estimated individual effect may be taken from a concentration-response relationship derived on the basis of dose-response observations. It has to be noted that, in mixtures of many substances, the effects to be estimated for the individual contributors become rather small therefore, a high-quality estimation of the concentration response, particularly in the low effect region, is needed. In such cases, it might be useful to consider models other than the standard probit or logit functions for description of the data. 

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