Usually not recommended well get back to this the

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usually not recommended (we’ll get back to this) The modification indices are very large for paths to S-C CAPS (Straight-Curved Capitals) from Visual, and correlation between the error term in COUNTDOT and ADDITION. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 33 / 54
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An empirical example: Mental abilities In order to modify the model, the modifications needs to be well-founded in substantial theoretical knowledge of the data. Out of Stata’s several suggestions, only letting “S-C CAPS” be a measure-variable of Visual ability made sense to the researchers: The test in Straight-Curved Capitals is a mixture between Speed in numerics using visual ability. Because this change was theoretically well-founded, the researchers modified the model and freed this parameter. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 34 / 54
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An empirical example: Mental abilities The modified now passes the strict Chi-Square goodness-of-fit test, indicating a very good fit. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 35 / 54
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An empirical example: Mental abilities Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 36 / 54
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An empirical example: Mental abilities Here R 2 has the same interpretation as the commonalities in EFA and is the percent of variance explained by the factor model Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 37 / 54
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An empirical example: Mental abilities A “rule of thumb” is that R 2 should be above 50 % , but this varies from discipline to discipline. Variable: VIS PERC CUBES LOZENGES Measures: Visual Visual Visual R 2 0.502 0.233 0.422 Variable: PAR COMP SEN COMP WORDMEAN Measures: Verbal Verbal Verbal R 2 0.753 0.689 0.681 Variable: ADDITION COUNTDOT S-C CAPS Measures: Speed calc. Speed calc. Speed calc. and visual R 2 0.455 0.752 0.529 R 2 is very low for the cubes-test, and this indicate that this test is not very good as a measurement-variable. The tests measuring verbal abilities are generally acceptably high. While each test may not be perfect, several tests can be combined to yield better measurements all in all. One can then combine these measurements to estimate an individual’s e.g. visual ability (but we will not). Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 38 / 54
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An empirical example: Mental abilities All constructs are positively correlated . Recall: Correlation > 0 means variables most often exceed or are below their means at the same time . Visual and verbal ability have moderately high positive correlation (0 . 558). Speed in numerics is positively correlated to both visual and verbal ability, but less so. Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 39 / 54
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Contents 1 Confirmatory factor analysis Stata: Inputting data based on empirical covariance matrices Inference, goodness of fit and modification indices An empirical example: Mental abilities 2 More on Path models Indirect and direct effects A brief empirical example from sociology On R 2 Steffen Grønneberg (BI) Lecture 11, GRA6036 17th March 2016 40 / 54
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Indirect and direct effects Consider the following path-model Systems with loops (or correlated error-terms) are called non-recursive path models.
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