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** Index**

Underlying all of the later
developments of the biometrical-genetical, path-analytic and factor-analytic
research programs
has
been a concern for the statistical problems of estimation
and hypothesis-testing. It is one thing to develop models; to attach the most
efficient and reliable numerical values to the effects specified in a model,
and to decide whether a particular model gives an adequate account of the
empirical data, are completely different. All three traditions that we have
identified as being relevant to our work rely heavily on the statistical
concept of likelihood, introduced by Ronald Fisher as a basis for developing
methods for parameter estimation and hypothesis
testing. The approach of ``maximum likelihood''
to estimation in human quantitative genetics was
first introduced in a landmark paper by Jinks and Fulker
(1970) in which they
first applied the theoretical and statistical methods of biometrical genetics
to human behavioral data. Essential elements of their understanding were that:
- complex models for human variation could be simplified
under the assumption of polygenic inheritance
- the goodness-of-fit of a
model should be tested before waxing lyrical about the substantive importance
of parameter estimates
- the most precise estimates of parameters should be
obtained
- possibilities exist for specifying and analyzing gene action
and genotype environment interaction

It was the
confluence of these notions in a systematic series of models and methods of
data analysis which is mainly responsible for breaking the intellectual
gridlock into which human behavioral genetics had driven itself by the end of
the 1960's.
Essentially the same statistical concern was found among those
who had followed the path analytic and factor analytic approaches.
Rao, Morton, and Yee (1974) used an approach close to
maximum likelihood for estimation of parameters in path models for the
correlations between relatives, and earlier work on the analysis of
covariance structures by Karl Jöreskog
had provided some of the first workable computer algorithms for
applying the method of maximum likelihood to parameter estimation and
hypothesis-testing in factor analysis.
Guided by Jöreskog's influence, the specification and testing of
specific hypotheses about factor rotation became possible. Subsequently,
with the collaboration of Dag Sörbom,
the analysis of covariance structures became elaborated into
the flexible model for Linear Structural Relations (LISREL) and
the associated computer algorithms which, over two decades, have
passed through a series of increasingly general versions.
The attempts to bring genetic methods to bear on psychological
variables naturally led to a concern for how the psychometrician's
interest in multiple variables could be reconciled with the
geneticist's methods for separating genetic and environmental effects.
For example, several investigators (Vandenberg, 1965; Loehlin and
Vandenberg, 1968; Bock and Vandenberg, 1968)
in the late 1960's began to ask
whether the genes or the environment was mainly responsible for the
general ability factor underlying correlated measures of cognitive
ability. The approaches that were suggested, however, were relatively
crude generalizations of the classical methods of univariate twin data
analysis which were being superseded by the biometrical and path
analytic methods. There was clearly a need to integrate the model
fitting approach of biometrical genetics with the factor model which
was still the conceptual framework of much multivariate analysis in
psychology. In discussion with the late Owen White, it became clear
that Jöreskog's analysis of
covariance structures provided the necessary statistical formulation.
In 1977, Martin and Eaves
reanalyzed twin data on
Thurstone's Primary Mental Abilities using their
own FORTRAN program for a multi-group extension of
Jöreskog's model to twin data
and, for the first time, used the model fitting strategy of
biometrical genetics to test hypotheses, however simple, about the
genetic and environmental causes of covariation between multiple
variables. The subsequent wide dissemination of a multi-group version
of LISREL (LISREL III) generated a rash of demonstrations that what
Martin and Eaves had achieved somewhat
laboriously with their own program
could be done
more easily with LISREL (Boomsma and
Molenaar, 1986, Cantor, 1983;
Fulker *et al.*, 1983; Martin *et al.*, 1982; McArdle *
et al*, 1980). After teaching several workshops and applying LISREL
to everyday research problems in the analysis of twin and family data,
we discovered that it too had its limitations and was quite cumbersome
to use in several applications. This led to the development of Mx,
which began in 1990 and which has continued throughout this decade.
Initially devised as a combination of a matrix algebra interpreter and
a numerical optimization package, it has simplified the specification
of both simple and complex genetic models tremendously.
In the 1980's there were many significant new departures in the
specification of multivariate genetic models for family resemblance.
The main emphasis was on extending the path models, such as those of
Cloninger *et al.*, (1979a,b) to the
multivariate case (Neale &
Fulker, 1984; Vogler, 1985). Much of this work
is described clearly and in detail by Fulker
(1988) . Many of the models described could not be
implemented with the methods readily available at the time of writing
of the first edition this book. Furthermore, several of the more
difficult models were not addressed in the first edition because of
the lack of suitable data. Since that time many of the problems of specifying
complex models have been solved using Mx, and this edition presents some
of these developments. In addition, several research groups have now
gathered data on samples large and diverse enough to exploit most of
the theoretical developments now in hand.
The collection of large volumes of data in a rich variety of twin
studies from around the world in the last ten years, coupled with the
rocketing growth in the power of micro-computers, offer an
unprecedented opportunity. What were once ground-breaking methods,
available to those few who knew enough about statistics and computers
to write their own programs, can now be placed in the hands of
teachers and researchers alike.

** Next:** 2 Data Preparation
** Up:** 6 The Context of
** Previous:** 4 Integration of the
** Index**
Jeff Lessem
2002-03-21