The POWER Procedure

Analyses in the LOGISTIC Statement

Likelihood Ratio Chi-Square Test for One Predictor (TEST=LRCHI)

The power computing formula is based on Shieh and O’Brien (1998), Shieh (2000), and Self, Mauritsen, and Ohara (1992).

Define the following notation for a logistic regression analysis:

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The logistic regression model is

$\text{[math]}$

The hypothesis test of the first predictor variable is

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	$\text{[math]}$	$\text{[math]}$

Assuming independence among all predictor variables, $\text{[math]}$ is defined as follows:

$\text{[math]}$

where $\text{[math]}$ is calculated according to the following algorithm:

	$\text{[math]}$
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This algorithm causes the elements of the transposed vector $\text{[math]}$ to vary fastest to slowest from right to left as $\text{[math]}$ increases, as shown in the following table of $\text{[math]}$ values:

$\text{[math]}$

The $\text{[math]}$ values are determined in a completely analogous manner.

The discretization is handled as follows (unless the distribution is ordinal, or binomial with sample size parameter at least as large as requested number of bins): for $\text{[math]}$ , generate $\text{[math]}$ quantiles at evenly spaced probability values such that each such quantile is at the midpoint of a bin with probability $\text{[math]}$ . In other words,