Estimation methods for parametric growth curves
main topic
 

Minitab estimates the shape and scale using one of three estimation methods: maximum likelihood, conditional maximum likelihood, and least squares.

The log-likelihood is a measure of the fit of the distribution. When estimating the shape and scale parameters, Minitab will make this number as large as possible. By maximizing the likelihood function, Minitab calculates the maximum likelihood and conditional maximum likelihood estimates.

Minitab displays output in the Session window based on the chosen estimation method and whether or not the shape parameter is known. The differences are shown in the table below:

Method

Shape

Parameter estimates

Standard error and confidence intervals

Maximum likelihood

Unknown

Shape and scale

Yes

Maximum likelihood

Known, = 1

MTBF

Yes

Maximum likelihood

Known, not 1

Scale

Yes

Conditional maximum likelihood

Unknown

Shape and scale

For shape only

Least squares

Unknown

Shape and scale

No

Least squares

Known, = 1

MTBF

No

Least squares

Known, not 1

Scale

No

 

See Comparison of growth curve procedures for a discussion of the advantages and disadvantages of each method.