Nonrecursive models—Page 1
Nonrecursive models
[NOTE: This lecture borrows heavily from Duncan’s Introduction to Structural Equation Models
and from William D. Berry’s Nonrecursive Causal Models.
Advantages and Disadvantages of Recursive Models.
We have previously considered
recursive models such as the following:
X1
X2
X3
X4
u
v
w
Recursive models meet the following conditions:
Models are hierarchical. All causal effects in the model are ―unidirectional‖ in nature, i.e. no
two variables in the model are reciprocally related, either directly or indirectly. Hence, the
first endogenous variable is affected only by the exogenous variables. The 2nd endogenous
variable is affected only by the exogenous variables and the first endogenous variable; and so
on.
All pairs of error (or disturbance) terms in the model are assumed to be uncorrelated.
j
will be uncorrelated with all explanatory variables in the equation containing
j
. In the
above, u is uncorrelated with X1; v is uncorrelated with X1 and X2; and w is uncorrelated
with X1, X2 and X3. (The disturbances can and generally will be correlated with X’s that
appear later in the model, e.g. u affects X2 which in turn affects X3, so u and X3 are
correlated: u is an indirect cause of X3.)
Let L = # of variables in a model (in this case 4). Recall that, for L variables, the number of
unique variances and covariances = (L*[L+1]/2). So, in the above model, there are 10 unique
variances and covariances. Note too that in the above, there are 10 structural parameters: 1
exogenous variance, 6 betas, and three disturbance variances. The above model is
just
identified
. If there were fewer structural parameters than there were covariances (e.g. if one or
more of the betas = 0) the model would be
overidentified
. The optional Appendix A of this
handout discusses identification further and how it provides an alternative view of hypothesis
testing.
An advantage of recursive models is that they are easy to estimate. All recursive models are
identified. OLS regression can be used to obtain unbiased estimates of the model’s coefficients.
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View Full DocumentNonrecursive models—Page 2
Unfortunately, in many situations the assumptions of recursive models are not realistic. Consider
the following model:
Policy & Issue positions
Comparative Candidate
v
Evaluation
Political Party ID
u
According to this model, policy and issue positions affect an individual’s party affiliation. Each
of these in turn affects how candidates are evaluated. The assumptions of the model may not be
reasonable.
While party id may influence evaluation of candidates, it may also be the case that candidate
evaluations affect party id, e.g. if you like a candidate, you may be more likely to identify
with that candidate’s party.
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 Spring '11
 RichardWilliams
 Regression Analysis, R Square, sig t, Nonrecursive models—Page, Nonrecursive Models

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