Detailed Outline
Abbreviated Outline
I. Overview(page 106)
Focus:
How ML methods work
Two alternative ML approaches
Guidelines for choice of ML approach
Overview of statistical inferences
II. Background about maximum likelihood procedure
(pages 106–107)
A. Alternative approaches to estimation: least
squares (LS), maximum likelihood (ML), and
discriminant function analysis.
B. ML is now the preferred method – computer
programs now available; general applicability of
ML method to many different types of models.
III. Unconditional vs. conditional methods(pages
107–111)
A. Require different computer programs; user must
choose appropriate program.
B. Unconditionalpreferred if number of parameters
smallrelative to number of subjects, whereas
conditionalpreferred if number of parameters
largerelative to number of subjects.
C. Guidelines: use conditional if matching; use
unconditional if no matching and number of
variables not too large; when in doubt, use
conditional – always unbiased.
IV. The likelihood function and its use in the ML
procedure(pages 111–117)
A. L¼L(u)¼likelihood function; gives joint prob-
ability of observing the data as a function of the set
of unknown parameters given byu¼(y 1 ,y 2 ,...,
yq).
B. ML method maximizes the likelihood function
L(u).
C. ML solutions solve a system ofqequations inq
unknowns; this system requires aniterative
solution by computer.
D. Two alternative likelihood functions for logistic
regression: unconditional (LU) and conditional
(LC); formulae are built into unconditional and
conditional computer algorithms.
E. User inputs data and computer does calculations.
F. Conditional likelihood reflects the probability of
observed data configuration relative to the prob-
ability of all possible configurations of the data.122 4. Maximum Likelihood Techniques: An Overview