Estimation of the unstandardized effects of causal models

In many cases, researchers are interested in the unstandardized coefficients, which can be obtained by analyzing the raw data or the covariance matrix. In this chapter, we will therefore show how the analysis can be done, starting with the covariance matrix of the observed variables of interest. The first step is the estimation of the covariance matrix weighted for design weights, as we did for the correlation matrix. The second step is correction of the covariances and variances for measurement error. After that, the unstandardized coefficients can be estimated as before.

The covariance matrix can easily be estimated using any statistical program. For those interested in reproducing the results of this module, the procedure and the syntax are provided in the following links for both SPSS and Stata, using a dataset especially prepared for this module.

Covariance matrix in SPSS

  1. In the following link, you will find the dataset ‘CME data – ESSround 6’.
    Download data in SPSS format
    Open this dataset in SPSS:1
    GET FILE='C:\...\CME data_ESSround6.sav'.
  2. First, select the cases under study in our analysis. They concern the whole British population. Therefore, from Data in SPSS, select ‘Select Cases…’. To limit the analysis to Great Britain, choose ‘If condition is satisfied, select the variable ‘Country’ and insert the following notation: cntry = ‘GB’.
    COMPUTE filter_$=(cntry="GB").
    VARIABLE LABELS filter_$ 'cntry="GB" (FILTER)'.
    VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'.
    FORMATS filter_$ (f1.0).
    FILTER BY filter_$.
    EXECUTE.
  3. Under Data, you have to weight the cases using design weights. Select ‘Weight cases’ and weight the cases by the variable ‘Design weight [dweight]’.
    WEIGHT BY dweight.
  4. To obtain the covariance matrix, choose ‘Correlate’ from Analyze and then click ‘Bivariate…’. From the list, select the variables in the following order: Satdem [stfdem], Free [fairelecc], Critic [oppcrgvc], Equal [cttresac], LRplace [lrscale] and Inc [hinctnta]. Once the variables are selected, in Options choose ‘Cross-product deviations and covariances’ to obtain the statistics of those variables and also choose the option ‘Exclude cases listwise’ to obtain the results for the same cases in the sample.
    CORRELATIONS
    /VARIABLES=stfdem fairelcc oppcrgvc cttresac lrscale hinctnta
    /PRINT=TWOTAIL NOSIG
    /STATISTICS XPROD
    /MISSING=LISTWISE.

This procedure should lead to the result in the following table:

Covariance matrix in Stata

  1. In the following link, you will find the dataset ‘CME data – ESSround 6’
    Download data in Stata format
    Open this dataset in Stata:2
    use "C:\...\CME data_ESSround6.dta", clear
  2. Select the cases under study. They concern the whole British population. Therefore, in Stata we can use the command ‘keep if’ and indicate that we will keep all observations that for the variable ‘Country (cntry)’ have the value ‘GB’.
    keep if cntry=="GB"
  3. Performing some tabulations of our variables of interest before seeing the descriptives, we see that the variables Satdem [stfdem], Free [fairelecc], Critic [oppcrgvc], Equal [cttresac], LRplace [lrscale] and Inc [hinctnta] have Refusal and Don’t know values, which should be assigned to system missing. This can be done using the command ‘mvdecode’.
    mvdecode stfdem fairelcc oppcrgvc cttresac lrscale hinctnta, mv(99)
    mvdecode stfdem fairelcc oppcrgvc cttresac lrscale hinctnta, mv(88)
    mvdecode stfdem fairelcc oppcrgvc cttresac lrscale hinctnta, mv(77)
  4. To obtain the descriptive statistics in Stata, we have used the command ‘corr’. Using this command, select the seven variables under analysis in the following order: Satdem [stfdem], Free [fairelecc], Critic [oppcrgvc], Equal [cttresac], LRplace [lrscale] and Inc [hinctnta]. Here, the design weights have been applied using the command ‘aweight’. Furthermore, in order to obtain the covariance matrix we add the notation ‘cov’.
    corr stfdem fairelcc oppcrgvc cttresac lrscale hinctnta [aweight=dweight], cov

This procedure should lead to the result in the following table:

Table 6.1: The covariances between the variables from the satisfaction with democracy model of ESS Round 63 for Great Britain corrected by design weights (n=1468)4.

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Footnotes