Reporting Regression Results from SEM output

[Rafaela Boldt]

Dear all,

my supervisor told me I should report the regression results from my SEM model.
I know I can report the p-value and I think (but I am totally not sure) that the Estimate-Value is equal my Beta value.
I don't see any R-squared values etc. which are needed to report a regression.
Can anyone help me, whether it is possible to get those values?

This table shows an example of my regression results:

 Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all

Regressions:
  WLB ~
    SUSU              0.005    0.010    0.517    0.605    0.051    0.051
    JOBI             -0.056    0.014   -4.084    0.000   -0.357   -0.357
    FSOP              0.021    0.019    1.135    0.257    0.103    0.103
    PI               -0.020    0.012   -1.608    0.108   -0.154   -0.154
    WHSI             -0.004    0.012   -0.310    0.756   -0.028   -0.028
    HWSI              0.009    0.010    0.936    0.349    0.090    0.090

Thank you in advance!!
Rafaela

[Ashenafi Kassahun]

Hi,

I guess, if you want to report the standardized estimate the last column (std.all) is the right one. If you want the unstandardized coefficeint, the first column (Estimate). You may also report both. However, it seems you have only one significant regression; WLB from JOBI, β=-.357. 

Ashenafi

[Rafaela Boldt]

Thank you for your answer.

So but I can not report any F or t-statistics, correct? I can just say, that there is a sign. regression with a b/beta-value of XY?

Rafaela

[Ashenafi Kassahun]

If you look at the output of your model, in the upper part, you will find the chi sq. and other model fit indices in addition to the regression path. You may need to report the chi sq., CFI, RMSEA...

Ashenafi

[Mikko Rönkkö]

Hi

You can get R2’s using the summary-method. See http://www.jstatsoft.org/v48/i02/paper

The z-statistic, which you can see in your results, is calculated in the exact same way as the t-statistic and they are also nearly identically distributed if sample size is over 30 or so. In regression, the sampling distribution of the ratio of estimated coefficients and SEs follows the t-distribution in small samples when the model assumptions hold. The problem with more complex models, such as SEMs, is that the proofs exists only for large sample scenarios, which would lead to z-statistic. Therefore, reporting t-statistics would not be appropriate. 

For the same reason I do not think that using the F-statistic is appropriate in SEM context.

Mikko

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[Rafaela Boldt]

Thank you!!

I calculated R2 but my output does not include R2 for my regressions, just for each dependent variable....Do you know if I can get R2 for each regression as well?

Rafaela

[Mikko Rönkkö]

Hi

Can you clarify what you mean. Each regression has one dependent variable, and the R2 tells how much the independent variables explain that dependent variable.

Mikko

[Rafaela Boldt]

Hi,

I want to know how much variance the regression equation can explain. 
I mean those regressions:

Regressions:
  WLB ~
    SUSU              0.170    0.054    3.152    0.002    0.307    0.307
    JOBI             -0.290    0.080   -3.635    0.000   -0.341   -0.341
    FSOP              0.153    0.147    1.046    0.296    0.114    0.114
    PI                0.041    0.098    0.421    0.674    0.040    0.040
    WHSI             -0.018    0.072   -0.246    0.805   -0.022   -0.022
    HWSI             -0.021    0.043   -0.495    0.620   -0.044   -0.044


and not those one's:

PERF =~ IRB1 + IRB2 + IRB3 + IRB4 + OCBI1 + OCBI2 + OCBI3 + OCBI4 + OCBI5 + OCBI6 + OCBI7 + OCBI8
INTL =~ IL

--> here the R2 gives me information about how much the independent variables explain.

But I want to know, about the varianz of the regression of the dependent variables.

Do you know what I mean?

Rafaela

[Terrence Jorgensen]

I want to know how much variance the regression equation can explain.  

You mean an r-squared for each predictor?  Look in the "std.all" column for the standardized regression slopes.  Those are semipartial correlation coefficients (r), which you can square if you think that tells you something different from the unsquared r.  Try saving the data.frame returned by parameterEstimates() and adding a column that is the square of the "std.all" column.

But that r-squared can only be interpreted as "the proportion of variance in the outcome explained by that single predictor" when the predictors themselves do not share any variance (r = 0), which (realistically) can only be the case when you have control over the predictors (e.g., balanced random assignment to conditions in a factorial design).

Terry

[Mikko Rönkkö]

Hi

Just to clarify, this

Regressions:
  WLB ~
    SUSU              0.170    0.054    3.152    0.002    0.307    0.307
    JOBI             -0.290    0.080   -3.635    0.000   -0.341   -0.341
    FSOP              0.153    0.147    1.046    0.296    0.114    0.114
    PI                0.041    0.098    0.421    0.674    0.040    0.040
    WHSI             -0.018    0.072   -0.246    0.805   -0.022   -0.022
    HWSI             -0.021    0.043   -0.495    0.620   -0.044   -0.044

is just one multiple regression equation. It has one dependent variable, and 6 independent variables, and one R2 (squared multiple correlation) value. Regression does not have R2 for each independent variable, there is just one R2 for the full equation. (But see what Terry says about the semi partial correlations.)

Mikko

[Rafaela Boldt]

It's me again...

My supervisor says I should get a t-value from the output, which I need to report in the field of the beta values...
But I only see z-values, thats it....

Can you help me if there is any t value in the output?

Thank you so much!!

Rafaela

Am Freitag, 10. April 2015 13:02:29 UTC+2 schrieb Ashenafi Kassahun:

[Edward Rigdon]

Eafaela—

     The difference between t and z is a matter of sample size—as sample size increases, the t distribution converges on a z distribution.  Factor-based SEM is generally a large sample methodology, so that the distinction between t and z should be minimal.  That is why you only see z values.  (in the old LISREL package, they were called t values, but were really z values even there.)

--Ed Rigdon

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[Rafaela Boldt]

Thank you Ed, that really helps!

Best regards
Rafaela