Page 529 - Encyclopedia of Nursing Research

496 n STRUCTURAl eQUATIOn mODelIng

lagged paths from three or more time points. on the inclusion of omitted paths (causal or
The path from latent variable A at Time 1 to correlational). Any path that is omitted speci-
S latent variable B at Time 2 can be set to equal fies that there is no relationship, implying a
the path from latent variable A at Time 2 to parameter of zero; thus, analysis programs
latent variable B at Time 3. equality con- constrain these paths to be zero. After esti-
strains also are used to compare models for mating the specified model, most programs
two or more different groups. For example, provide a numerical estimate of the “strain”
to compare the models of effects of maternal experienced by fixing parameters to zero or
employment on preterm and full-term child improvement in fit that would result from
outcomes, paths in the preterm model can be freeing the parameters (allowing them to
constrained to be equal to the corresponding vary). Suggested paths must be theoretically
paths in the full-term model. defensible before adding them to the respeci-
Data requirements for Sem are simi- fied model.
lar to those for factor analysis and multiple Because model respecification is based
regression in level of measurement but not on the data at hand in light of theoretical evi-
sample size. exogenous variables can have dence and those data are repeatedly tested,
indicators that are measured as interval, the significance level of the χ is actually
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near interval, or categorical (dummy-, effect-, higher than what the program indicates.
or orthogonally coded) levels, but endog- Thus, other criteria are necessary to evalu-
enous variables must have indicators that ate the adequacy of the final model. First is
are measured at the interval or near-interval the theoretical appropriateness of the final
level. The rule of thumb regarding the num- model. Comparison of the original model
ber of cases needed for Sem, 5 to 10 cases per with the final model will indicate how much
parameter to be estimated, suggests consid- “trimming” has taken place. In addition,
erably larger samples than usually needed the values and signs of the parameters are
for multiple regression; thus, samples of 100 evaluated. The signs (positive or negative)
for a very modest model to 500 or more for of the parameters should be in the expected
more complex models are often required. direction. parameters on the paths between
Despite the advantages of Sem, these larger the latent variable and its indicators should
samples can result in complex and costly be >.50 but <1.0 in a standardized solution.
studies. The lower the unexplained variance of the
Sem is generally a multistage procedure. endogenous variables, the better the model
First, the Sem implied by the theoretical performed in explaining those endogenous
model is tested and the fit of the model to the variables (similar to the 1–R value in mul-
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observed data is evaluated. A nonsignificant tiple regression). Results that are consistent
χ indicates acceptable fit, but this is diffi- with a priori expectations and findings from
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cult to obtain because the χ value is heavily previous research increase one’s confidence
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influenced (increased) by larger sample sizes. in the model.
Thus, most analytic programs provide other In summary, Sem is a powerful and flex-
measures of fit. A well-fitting model is nec- ible analysis technique for testing models of
essary before the parameter estimates can be cause, for investigating specific cause-and-
evaluated and interpreted. effect relationships, and for exploring the
In most cases, the original theoretical hypothesized process by which specific out-
model does not fit the data well, and modi- comes are produced. With Sem programs,
fications must be made to the model in order the researcher has greater control over the
to obtain a well-fitting model. Although dele- analyses than with other factor analysis
tion of nonsignificant paths (based on t val- and multiple regression programs. model
ues) is possible, modifications generally focus respecification is usually necessary, but the