l93 - Nonrecursive models [NOTE: This lecture borrows...

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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 over-identified . 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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Nonrecursive 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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This note was uploaded on 02/29/2012 for the course SOC 63993 taught by Professor Richardwilliams during the Spring '11 term at Notre Dame.

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l93 - Nonrecursive models [NOTE: This lecture borrows...

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