In matrix form we have the following table of effects

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In matrix form, we have the following table of effects. We usually only care about effects between the latent variables. Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 26 / 37
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Contents 1 Finishing the R 2 -discussion 2 General SEM General SEMs: Introduction and diagram conventions An empirical example SEM-theory Statistical estimation of SEMs Model assessment and modification Direct and indirect effects An empirical example Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 27 / 37
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An empirical example Recall our example on the feeling of alienation. Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 28 / 37
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An empirical example We first investigate the measurement model This is a standard CFA which we know how to work with. Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 29 / 37
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An empirical example Stata-code: clear a l l ssd i n i t ANOMIA67 POWERL67 ANOMIA71 POWERL71 EDUC SEI ssd set observations 932 # d e l i m i t ; ssd set covariances 11.834 \ 6.947 9.364 \ 6.819 5.091 12.532 \ 4.783 5.028 7.495 9.986 \ - 3.839 - 3.889 - 3.841 - 3.625 9.610 \ - 2.190 - 1.883 - 2.175 - 1.878 3.552 4.503 ; # d e l i m i t cr sem ( Alien67 - > ANOMIA67, ) ( Alien67 - > POWERL67, ) ( Alien71 - > ANOMIA71, ) ( Alien71 - > POWERL71, ) ( Ses - > EDUC, ) ( Ses - > SEI , ) , covstruct ( lexogenous , diagonal ) l a t e n t ( Alien67 Alien71 Ses ) cov ( Alien67 * Alien71 Alien67 * Ses Alien71 * Ses ) nocapslatent Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 30 / 37
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An empirical example The model does not fit well to the data. The Chi-square test is rejected, and the RMSEA is > 0 . 10. Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 31 / 37
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An empirical example Stata prints the following modification indices. The total Chi-Square is 71.47, so these are very large modification indices. When the same theoretical construction (such as feeling of alienation) is measured repeatedly by the same tests, the error variables are often correlated due to re-test effects. It is reasonable that the measurement errors for the two similar tests in 67 and 71 correlate. Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 32 / 37
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An empirical example The researchers freed the correlation between the error terms in 67 and 71, and suggested the following modified (full SEM) model. The measurement model now passes the Chi-Square-test, indicating a very good fit. (One of the freed error-correlations are insignificant, and may be removed to get a more parsimonious model, but the researchers stuck to the full model.) Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 33 / 37
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An empirical example The measurement model: The model fits well to data with “LR test of model vs. saturated: chi2(4) = 4.74, Prob > chi2 = 0.3151” Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 34 / 37
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An empirical example The full SEM model: Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 35 / 37
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An empirical example Steffen Grønneberg (BI) Lecture 12, GRA6036 31st March 2016 36 / 37
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An empirical example The relationships between the assumptions on the latent variables in the measurement model and the full model corresponds to comparing the saturated model ( Σ free) and a candidate path model.
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