Proc Logistic - Analysis of Maximum Likelihood Estimates

[vishal_prof_gmail_com]

Hi,

In Proc Logistics output we get the Analysis of Maximum Likelihood Estimates which gives parameter coefficients. My questions is what is the relation between Estimates , Standard Error and Wald Chi Square statistic.

In Linear Regression Standard Error means the diffference between Sample mean and population mean. What does Standard error signify here.

Vishal

[Ksharp]

From my understanding, Standard Error is the Standard Deviation of Statistic . Which measure the accuracy of parameter coefficient, The smaller is the better. Wald Chi Square measure the Hypothesis H0: parameter coefficient=0

[lvm]

A standard error is the square root of the variance of a sampling distribution for the estimated parameter (the distribution of an estimated parameter). That is, a parameter is a constant but its estimate is a random variable (its distribution is called the sampling distribution). SE has the same meaning whether one is using moments, least squares, or maximum likelihood to estimate a parameter.

A Wald chi-square statistic is the square of the parameter estimate divided by its SE.

[Rick_SAS]

To build on what @lvm said, a parameter is a population value. A STATISTIC (which lvm calls a parameter estimate) is a random variable that depends on a random sample that is drawn from a population. The statistic has a distribution, which reflects that fact that if you choose a different random sample, you will obtain a different estimate. The collection of all estimates, taken over all random samples of a particular size, can be described by the probability distribution of the statistic, which is called the sampling distribution. 

The standard error of a statistic is the standard deviation of the samping distribution. For simple statistics, the sampling distribution is known asymptotically (that is, for very large samples). For other statistics, you need to assume that the population is normally distributed if you want an approximate formula for the standard error.