User:Sharp-shinned.hawk/sandbox/Structural Equation Modeling
is a general term used to describe a family of statistical methods designed to test a conceptual or theoretical model.{{sfn|Kaplan|2007|p=79-88}} Some common SEM methods include confirmatory factor analysis, path analysis, and latent growth modeling.{{sfn|Kline|2011}} The term "structural equation model" most commonly refers to a combination of two things: a "measurement model" that defines latent variables using one or more observed variables, and a "structural regression model" that links latent variables together.{{sfn|Kaplan|2007|p=79-88}} {{sfn|Kline|2011|p=230-294}} The parts of a structural equation model are linked to one another using a system of simultaneous regression equations.{{sfn|Kline|2011|p=265-294}}
SEM is widely used in the social sciences because of its ability to isolate observational error from measurement of latent variables.{{cite journal|last1=Hancock|first1=Gregory|title=Fortune Cookies, Measurement Error, and Experimental Design|journal=Journal of Modern Applied Statistical Methods|volume=2|issue=2|pages=293-305|url=http://digitalcommons.wayne.edu/jmasm/vol2/iss2/3/|accessdate=24 January 2015}} To provide a simple example, the concept of human intelligence cannot be measured directly as one could measure height or weight. Instead, psychologists develop theories of intelligence and write measurement instruments with items (questions) designed to measure intelligence according to their theory.{{cite book|last1=Thorndike|first1=Robert|editor1-last=Salkind|editor1-first=Neil|editor1-link=J|title=Encyclopedia of Measurement and Statistics|date=2007|publisher=Sage|isbn=9781412952644|pages=477-480|url=http://dx.doi.org/10.4135/9781412952644|chapter=Intelligence Tests}} They would then use SEM to test their theory using data gathered from people who took their intelligence test. With SEM, "intelligence" would be the latent variable and the test items would be the observed variables.
A simplistic model suggesting that intelligence (as measured by five questions) can predict academic performance (as measured by SAT, ACT, and high school GPA) is shown below. In SEM diagrams, latent variables are commonly shown as ovals and observed variables as rectangles. The below diagram shows how error (e) influences each intelligence question and the SAT, ACT, and GPA scores, but does not influence the latent variables. SEM provides numerical estimates for each of the parameters (arrows) in the model to indicate the strength of the relationships. Thus, in addition to testing the overall theory, SEM therefore allows the researcher to diagnose which observed variables are good indicators of the latent variables.
Modern studies usually test much more specific models involving several theories, for example, Jansen, Scherer, and Schroeders (2015) studied how students' self-concept and self-efficacy affected educational outcomes.{{cite journal|last1=Jansen|first1=Malte|last2=Scherer|first2=Ronny|last3=Schroeders|first3=Ulrich|title=Students' self-concept and self-efficacy in the sciences: Differential relations to antecedents and educational outcomes|journal=Contemporary Educational Psychology|date=April 2015|volume=41|pages=13-24|doi=doi:10.1016/j.cedpsych.2014.11.002}} SEM is also used in the sciences,{{cite book|last1=Gillespie|first1=David|last2=Perron|first2=Brian|editor1-last=Boslaugh|editor1-first=Sarah|title=Encyclopedia of Epidemiology|date=2007|publisher=Sage|isbn=9781412953948|pages=1005-1009|url=http://dx.doi.org/10.4135/9781412953948|chapter=Structural Equation Modeling}} business,{{cite book|last1=Markus|first1=Keith|editor1-last=Rogelberg|editor1-first=Steve|editor1-link=G.|title=Encyclopedia of Industrial and Organizational Psychology|date=2007|publisher=Sage|isbn=9781412952651|page=774-777|url=http://dx.doi.org/10.4135/9781412952651|chapter=Structural Equation Modeling}} education,{{cite book|last1=Shelley|first1=Mack|editor1-last=English|editor1-first=Fenwick|title=Encyclopedia of Educational Leadership and Administration|date=2007|publisher=Sage|isbn=9781412939584|url=http://dx.doi.org/10.4135/9781412939584|chapter=Structural Equation Modeling}} and many other fields.
{{cite book|last1=Kaplan|first1=David|title=Structural Equation Modeling|date=2007|publisher=Sage|isbn=9781412950589|pages=1089-1093|url=http://dx.doi.org/10.4135/9781412950589}}
Old intro:
either of two computer based statistical fit software packages: PLS-PA and LISREL/AMOS software. The methods were developed as alternatives to the more widely used systems of regression equation approached used in econometrics.