Cumulative Response Models

For a row vector of explanatory variables , the linear predictor

     

is estimated by

     

where and are the MLEs of and . The estimated standard error of is , which can be computed as the square root of the quadratic form , where is the estimated covariance matrix of the parameter estimates. The asymptotic confidence interval for is given by

     

where is the percentile point of a standard normal distribution.

The predicted value and the confidence limits for Pr are obtained by back-transforming the corresponding measures for the linear predictor.

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Predicted Probability

Confidence Limits

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