Statistics Seminar
| Date/Time: | Monday, 02 Nov 2015 from 4:10 pm to 5:00 pm |
|---|---|
| Location: | Snedecor 3105 |
| Cost: | Free |
| URL: | www.stat/oastate/edi |
| Phone: | 515-294-3440 |
| Channel: | College of Liberal Arts and Sciences |
| Categories: | Lectures |
| Actions: | Download iCal/vCal | Email Reminder |
The beta distribution is a simple and flexible model in which responses are naturally confined to the finite interval (0,1). The parameters of the distribution can be related to covariates such as concentration and gender through a regression model. The Ballooned Beta-logistic model, with expected responses equal to the Four Parameter Logistic model, is introduced. It expands the response boundaries of the beta regression model from (0,1) to (L,U), where L and U are unknown parameters. Under the Ballooned Beta-logistic model, expected responses follow a logistic function, but it differs from the classical Four Parameter Logistic model, which has normal additive normal errors, with positive probability of response from to . In contrast, the Ballooned Beta-logistic model may have skewed responses with smaller response variances at more extreme covariate values and symmetric responses with relative large variance at central values of the covariate. It may also have monotone increasing or decreasing variances depending on parameter values. These features are common in bioassay data at different concentrations. The asymptotic normality of maximum likelihood estimators is proved even though the support of this non-regular regression model depends on unknown parameters. Given enzyme-linked immunosorbent assay data from different plates, the motivating validation objective is to set boundary criteria for estimates of L and U, after which plates with boundary estimates outside these limits would be considered "reference failures". We find maximum likelihood and least squares estimates converge faster to L and U than do extreme values at the minimum and maximum concentrations. We also find maximum likelihood estimators perform better than least squares estimators when the covariate range is not sufficiently wide.