Using Least Squares and Maximum Likelihood Estimation
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Minitab provides two methods to analyze the natural log of standard deviation (s): Least squares estimation (LS) and maximum likelihood estimation (MLE).

In many cases, the differences between the LS and MLE results are minor, and the methods can be used interchangeably. You may want to run both methods and see whether the results confirm one another. If the results differ, you may want to determine why. For example, MLE assumes that the original data are from a normal distribution. If your data are not normally distributed, LS can provide better estimates. Also, LS cannot calculate results for data that contain a standard deviation equal to zero. MLE may provide estimates for these data, depending on the model.    

One guideline for using LS and MLE together, for different parts of the analysis, is discussed in [7]. This approach states that LS provides better p-values for the effects, while MLE provides more precise coefficients. Based on this approach, follow these steps to conduct your analysis:

1    Use least squares regression to select the model, determining which terms are not significant from the p-values of the coefficients

2    Refit the model, excluding nonsignificant terms to identify the appropriate reduced model

3    Use MLE to estimate the final coefficients of the model and to determine the fits and the residuals

For more information on these methods or this approach, see [7].