Specify the options for Analyze Binary Response for Response Surface Design

Stat > DOE > Response Surface > Analyze Binary Response > Options

Specify the options to use to analyze your response surface design.

In This Topic

Link function
Weights
Confidence level for all intervals
Type of confidence interval
Residuals for diagnostics
Test for ANOVA table
Number of groups for Hosmer-Lemeshow test

Link function

Minitab provides three link functions, which let you fit a broad variety of binary response models. A link function is the inverse of a distribution function. You want to choose a link function that results in a good fit to your data. Examine the goodness-of-fit statistics in the output to compare how well the model fits your data using different link functions. You can also choose link functions for historical reasons or because they have a special meaning in your discipline. For more information, go to What is a link function?.

Logit: By default, Minitab uses the logit link function because it provides the most natural interpretation of the estimated coefficients and it provides estimates of the odds ratios.
Normit/Probit: Use the normit link function, which assumes that there is an underlying variable that follows a normal distribution that is classified into categories. For example, you assume that pesticide resistance is an unmeasurable characteristic of an insect that follows a normal distribution. However, instead of recording pesticide resistance, you classify insects into categories of survived and died at different doses of pesticide.
Gompit/Complementary log-log: Use the gompit function, which is the inverse of the Gompertz distribution function. If the logit or normit functions do not fit the data, the gompit function can sometimes provide an adequate fit because the gompit function is asymmetric.

Weights

In Weights, enter a numeric column of weights to perform weighted regression. The weights must be greater than or equal to zero. The weights column must have the same number of rows as the response column. For more information about determining the appropriate weight, go to Weighted regression.

Confidence level for all intervals

Enter the level of confidence for the confidence intervals for the coefficients and the fitted values. If you use the logit link function, this confidence level is also the confidence level for the confidence intervals for the odds ratios.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you took 100 random samples from the population, the confidence intervals for approximately 95 of the samples would contain the parameter that the interval estimates. For a given set of data, a lower confidence level produces a narrower interval, and a higher confidence level produces a wider interval.

Note

To display the confidence intervals for the coefficients and the fitted values, you must go to the Results sub-dialog box, and from Display of results, select Expanded tables.

Type of confidence interval

You can select a two-sided interval or a one-sided bound. For the same confidence level, a bound is closer to the point estimate than the interval. The upper bound does not provide a likely lower value. The lower bound does not provide a likely upper value.

Two-sided: Use a two-sided confidence interval to estimate both likely lower and upper values for the mean response.
Lower bound: Use a lower bound to estimate a likely lower value for the mean response.
Upper bound: Use an upper confidence bound to estimate a likely higher value for the mean response.

Residuals for diagnostics

The deviance and Pearson residuals help identify patterns in the residual plots and outliers. Observations that are poorly fit by the model have high deviance and Pearson residuals. Minitab calculates the residual values for each distinct factor/covariate pattern.

Deviance: Deviance residuals are a measure of how well the model predicts the observation. Deviance residuals are often preferred for a logistic regression that uses the logit link function because the distribution of the residuals is more like the distribution of residuals from least squares models. The logit link function is the most common link function.
Pearson: Pearson residuals are also a measure of how well the model predicts the observation. A common approach for identifying outliers is to plot the Pearson residuals by the order of the observations in the worksheet.

Test for ANOVA table

Select the test for the ANOVA table.

Wald test: The default Wald test works well in most cases.
Likelihood ratio test: Use this option if you prefer the Likelihood ratio test.

Type of deviance

Select a deviance for calculating the chi-square values and the p-values. It is most common to use the adjusted deviance. Use the sequential deviance to determine the significance of terms by the order that they enter the model.

Adjusted (Type III): Measures the reduction in the deviance for each term relative to a model that contains all the remaining terms.
Sequential (Type I): Measures the reduction in the deviance when a term is added to a model that contains only the terms before it.

Number of groups for Hosmer-Lemeshow test

Enter the number of groups for the Hosmer-Lemeshow test. If you leave this value blank, Minitab attempts to make 10 groups of equal size. Ten groups works well for most data sets.

The Hosmer-Lemeshow test is a goodness-of-fit test, which assesses the model fit by comparing the observed and expected frequencies. The test divides the data into groups by their estimated probabilities from lowest to highest, then performs a chi-square test to determine whether the observed and expected frequencies are significantly different. If the number of unique factor/covariate patterns is small or large, you may want to change the number of groups. For example, you can use fewer groups to increase the expected values within the groups. Alternatively, you can use more groups to see greater detail in the comparison of the observed and expected values. Hosmer and Lemeshow suggest using a minimum of 6 groups¹.

¹ D.W. Hosmer and S. Lemeshow (2000). Applied Logistic Regression. 2nd ed. John Wiley & Sons, Inc.