Lecture
- the method of structural equation modeling…
Like hierarchical structural modeling, structural modeling formally relies on the ideas of regression analysis. The fundamental difference: the complex multidimensionality of structural modeling, i.e. the possibility of specifying in the model many analogs of the dependent variable and the independent variable.
The task of structural modeling: testing the suitability of a theoretical model, i.e. its correspondence to the data observed in the study (the data being covariance matrices among the variables). Structural modeling is often aimed at testing causal hypotheses. It is confirmatory in character, not exploratory.
A two-plane representation of structural models is possible:
- as visual diagrams and schemes
- as systems of regression equations
There are observed variables (denoted by a rectangle) and latent variables (by a circle).
The observed ones serve to operationalize the latent ones. The interrelations between the observed and the corresponding latent variables are specified within measurement models.
In general terms, measurement models are systems of regression equations that predict the observed variables on the basis of the latent ones by means of computational methods.
Structural models, in turn, specify the pattern of interrelations between these kinds of variables, including an indication of which latent variables are exogenous (i.e. independent variables) and which are endogenous (i.e. dependent variables).
The modeling process includes four stages:
1) Model specification
The researcher specifies the pattern of interrelations among the variables
2) Model estimation
The selection of coefficient values corresponding to the given indices
3) Model evaluation
Suitability is assessed on the basis of fit indices
4) Modification
Carried out in the case of a mismatch between the model and the data.
An important feature of SEM is the possibility of testing alternative models by comparing their fit indices, which makes it possible to carry out a direct comparison of competing theories.
Among its advantages is the possibility of working with data that do not conform to a normal distribution and with missing data.
Missing data (MD) appear when, for some subjects, information on one or more variables is not provided.
They can be ignored, but this will have sad consequences, for example, a reduction in the power of the statistical test.
The problem of missing data.
If a psychologist uses only a single index of the property of interest (a mono-method), then the omission of an answer will lead to a complete absence of data – and that is a pity.
The use of multiple measurements of a property (a multi-method) partially overcomes this limitation. In general, missing data are bad; they are a threat to construct validity, internal validity…
One can distinguish systematic and non-systematic missing data. Rubin (the researcher, not the stone):
1) missing completely at random
the analog of non-systematic confoundings, everything is fine
2) missing at random
related to the observed variables and can be modeled on the basis of the values associated with the systematic confoundings of the missing data.
3) missing not at random
the analog of systematic confoundings, the worst case.
Strategies for solving the problem of missing data:
- planning
For example, the balanced spiral block design.
The mechanism of the missing data is specified, which leads to data missing completely at random, which can then be taken into account with the help of appropriate statistical procedures.
This is statistical control in correlational studies (QUESTION 26)
- prevention
one must keep the subjects happy, and then they will not run away
- statistical accounting and modeling
Modern methods of analyzing missing data are also based on replacing the missing data with data computed on the basis of the information available to researchers about other covariate variables, or on the basis of a theoretical distribution of the indices across the variables.
Example: the method of multiple imputation, which involves the iterative replacement of missing data with several new values on the basis of empirically obtained data.
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