Help: SEM goodness-of-fit

[Marie Sofie]

Hello! I have performed a sem analysis, and I have also tested the goodness of fit of my model with the Stata command of "estat gof, stats(all)". The outcome it has given me is confusing me. It is the first time I am performing this statistic, and although I have read the SEM Stata reference manul and also idre ucla article on that, I really do not understand how to interpret the chi2. Here is the outcome.
----------------------------------------------------------------------------
Fit statistic | Value Description
---------------------+------------------------------------------------------
Likelihood ratio |
chi2_ms(0) | 0.000 model vs. saturated
p > chi2 | .
chi2_bs(11) | 86.468 baseline vs. saturated
p > chi2 | 0.000
---------------------+------------------------------------------------------
Population error |
RMSEA | 0.000 Root mean squared error of approximation
90% CI, lower bound | 0.000
upper bound | 0.000
pclose | 1.000 Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
AIC | 20059.081 Akaike's information criterion
BIC | 20112.062 Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison |
CFI | 1.000 Comparative fit index
TLI | 1.000 Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals |
SRMR | 0.000 Standardized root mean squared residual
CD | 0.132 Coefficient of determination
----------------------------------------------------------------------------
*/

So my main question is : Why the chi2 reporting my model versus saturated model equals to 0.000. Does it mean that my independent variables contain measurement errors? In that case, how do I need to interpret the second chi2? baseline versus saturated. At first sight it seems to me that the model poorly fits the data, but I am not entirely sure.

Thank you so much for your help

Best

[Marcos Almeida]

Hello Sofie,

Please use the CODE delimiters to share output, as recommended in the FAQ.

The chi-square test indicates your model could be improved. We may also see the dfs.

But you didn't say much about the model neither the variables. In general, there are quite interesting GOF parameters but a low coefficient of determination. Something to reflect about.

[Richard Williams]

Like Marcos says, this is really really hard to read, plus we don't know anything about the model that was estimated. But your output does say

Likelihood ratio |
chi2_ms(0) | 0.000 model vs. saturated

That implies that whatever model you ran, it was equivalent to the saturated model, i.e. you estimated as many parameters as you had variances and covariances in the data. Your other fit stats suggest the same thing.

If you show us the sem command and more of the (legible) output, we might be able to say more. But double-check to make sure you were specifying the model you wanted.

For an excellent source on Stata sem, see

http://www.stata.com/bookstore/disco...g-using-stata/

[Marie Sofie]

[Hello. I will try to use dataex and also the option to present my question and data in a more legible way. Here is a sample of my data: clear
input float sanct byte militarism float inter byte(sex edu age employ income repdem libcons foreignnews)
4 1 3 1 4 1 1 11 2 2 4
5 3 4 1 3 2 3 6 2 3 4
6 4 4 2 3 1 6 11 3 2 3
6 2 5 2 2 1 6 11 2 1 6
2 5 2 2 4 1 6 8 3 2 6
4 1 3 2 4 1 6 1 . 4 4
2 4 4 2 2 1 6 8 3 2 5
4 2 3 2 3 1 1 3 2 1 4
4 3 3 1 4 1 6 6 3 2 4
4 3 6 2 4 2 1 8 3 3 5
3 3 1 2 4 5 2 4 4 4 4
4 3 2 1 4 2 1 3 3 3 4
6 1 3 2 3 2 2 2 3 2 5
3 2 3 1 4 1 6 6 2 4 7
3 3 2 1 2 1 6 6 2 2 6
6 4 5 1 2 1 1 4 3 1 5
4 1 4 2 4 2 2 9 3 1 6
5 3 5 2 4 2 1 8 3 4 5
2 2 2 1 2 1 3 11 4 1 7
4 2 3 2 3 2 1 2 3 2 6
3 2 2 2 3 3 1 4 3 1 4
6 3 3 1 4 2 4 1 2 4 5
5 1 4 1 2 1 2 11 2 5 3
6 3 6 2 3 1 6 6 3 2 6
6 2 4 1 4 1 6 3 1 4 3
5 1 5 2 3 1 6 5 2 4 4
5 2 1 1 2 1 1 2 . 2 7
6 3 1 1 4 3 1 4 2 6 5
end
label values sanct sanct
label def sanct 1 "strongly disapprove", modify
label def sanct 2 "disapprove", modify
label def sanct 3 "somewhat disapprove", modify
label def sanct 4 "somwhat approve", modify
label def sanct 5 "approve", modify
label def sanct 6 "strongly approve", modify
label values militarism militarism
label def militarism 1 "agree strongly", modify
label def militarism 2 "agree", modify
label def militarism 3 "agree somewhat", modify
label def militarism 4 "disagree somewhat", modify
label def militarism 5 "disagree", modify
label def militarism 6 "disagree strongly", modify
label values inter inter
label def inter 1 "disagree strongly", modify
label def inter 2 "disagree", modify
label def inter 3 "disagree somewhat", modify
label def inter 4 "agree somewhat", modify
label def inter 5 "agree", modify
label def inter 6 "agree strongly", modify
label values sex sex
label def sex 1 "male", modify
label def sex 2 "female", modify
label values edu edu
label def edu 1 "less than high school", modify
label def edu 2 "high school graduate", modify
label def edu 3 "high school", modify
label def edu 4 "associate's/junior college", modify
label def edu 5 "bachelor's", modify
label def edu 6 "graduate's (masters, mba, phd, md)", modify
label values age age
label def age 1 "18-25", modify
label def age 2 "26-35", modify
label def age 3 "36-45", modify
label def age 4 "46-55", modify
label def age 5 "56-65", modify
label values employ employ
label def employ 1 "employed for wages", modify
label def employ 2 "self-employed", modify
label def employ 3 "out of work and looking for work", modify
label def employ 4 "out of work but not looking for wor", modify
label def employ 5 "homemaker", modify
label def employ 6 "student", modify
label def employ 7 "retired", modify
label def employ 8 "other", modify
label values income income
label def income 1 "less than $10,000", modify
label def income 2 "$10,000-$19,999", modify
label def income 3 "$20,000-$29,999", modify
label def income 4 "$30,000-$39,999", modify
label def income 5 "$40,000-$49,999", modify
label def income 6 "$50,000-$59,999", modify
label def income 7 "$60,000-$69,999", modify
label def income 8 "$70,000-$79,999", modify
label def income 9 "$80,000-$89,000", modify
label def income 10 "$90,000-$99,999", modify
label def income 11 "$100,000-$149,999", modify
label def income 12 "more than $150,000", modify
label values repdem repdem
label def repdem 1 "republican", modify
label def repdem 2 "independent", modify
label def repdem 3 "democrat", modify
label def repdem 4 "another", modify
label values libcons libcons
label def libcons 1 "extremely liberal", modify
label def libcons 2 "liberal", modify
label def libcons 3 "slighly liberal", modify
label def libcons 4 "moderate, middle of the road", modify
label def libcons 5 "slighly conservative", modify
label def libcons 6 "conservative", modify
label def libcons 7 "extremely conservative", modify
label values foreignnews foreignnews
label def foreignnews 1 "once a year", modify
label def foreignnews 2 "2-3 times a year", modify
label def foreignnews 3 "once a month", modify
label def foreignnews 4 "2-3 times a month", modify
label def foreignnews 5 "once a week", modify
label def foreignnews 6 "2-3 times a week", modify
label def foreignnews 7 "daily", modify
[/then I performed this command:
clear all
ssd init sanct militarism inter treatment age sex edu employ income repdem libcons foreignnews /*variables*/
ssd set observations 611 /*observations*/

*Correlation matrix

#delimit ;
ssd set correlations
1\
0.0991 1\
0.2809 0.3513 1\
0.0128 0.0256 -0.0356 1\
0.1342 0.1173 0.0712 0.025 1\
-0.0484 -0.0846 -0.0567 0.0384 0.1524 1\
0.0938 -0.109 0.0169 -0.0291 0.1533 0.0985 1\
-0.0751 -0.0154 0.0239 0.0095 -0.2903 0.024 -0.2235 1\
0.1677 0.027 0.1639 -0.048 -0.0116 -0.0622 0.1518 -0.074 1\
-0.0518 -0.1985 -0.0433 -0.0065 -0.059 0.137 0.0451 0.0729 -0.0149 1\
-0.0003 0.3505 -0.0242 -0.0184 0.1353 -0.1398 -0.0703 -0.0894 -0.0453 -0.5675 1\
0.1747 -0.0032 0.0449 -0.0067 0.1271 -0.132 0.102 -0.0365 0.134 0.0096 -0.018 1;
#delimit cr
save ssdmatrix.dat, replace

* and later sem

clear
use ssdmatrix.dat /*use the correlation matrix input as data*/
ssd list
sem (sanct<- militarism inter treatment age sex edu employ income repdem libcons foreignnews), standardized /*model*/

* finally estat gof


estat gof, stats(all)

/* the outcome of the "goodness of fit statistics"

----------------------------------------------------------------------------
Fit statistic | Value Description
---------------------+------------------------------------------------------
Likelihood ratio |
chi2_ms(0) | 0.000 model vs. saturated
p > chi2 | .
chi2_bs(11) | 86.468 baseline vs. saturated
p > chi2 | 0.000
---------------------+------------------------------------------------------
Population error |
RMSEA | 0.000 Root mean squared error of approximation
90% CI, lower bound | 0.000
upper bound | 0.000
pclose | 1.000 Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
AIC | 20059.081 Akaike's information criterion
BIC | 20112.062 Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison |
CFI | 1.000 Comparative fit index
TLI | 1.000 Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals |
SRMR | 0.000 Standardized root mean squared residual
CD | 0.132 Coefficient of determination
----------------------------------------------------------------------------
*/

I hope it makes sense. I am analysing the data this way, because in my next model I am applying a tool to correct for measurement errors; therefore I use the correlation matrix. Thank you so much.
]
][/CODE]

[Marie Sofie]

Is it legible this way? I am still learning how to get my head around this forum? Thank you

[Dick Campbell]

----------------------------------------------------------------------------
Fit statistic | Value Description
---------------------+------------------------------------------------------
Likelihood ratio |
chi2_ms(0) | 0.000 model vs. saturated
p > chi2 | .
chi2_bs(11) | 86.468 baseline vs. saturated
p > chi2 | 0.000
---------------------+------------------------------------------------------
Population error |
RMSEA | 0.000 Root mean squared error of approximation
90% CI, lower bound | 0.000
upper bound | 0.000
pclose | 1.000 Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
AIC | 20059.081 Akaike's information criterion
BIC | 20112.062 Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison |
CFI | 1.000 Comparative fit index
TLI | 1.000 Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals |
SRMR | 0.000 Standardized root mean squared residual
CD | 0.132 Coefficient of determination
----------------------------------------------------------------------------

[Dick Campbell]

Whoops, I hit the send key before I meant to.

You are part way there. One way to get code tags to work properly is to highlight want you want to appear within code tags and then click on the code icon which is the #.

That said, in SEM terms you have estimated a regression equation. Your model:

sem (sanct<- militarism inter treatment age sex edu employ income repdem libcons foreignnews), standardized /*model*/

regresses sanct on a set of right side variables. Such a model will fit the data exactly as this piece of output shows:

Likelihood ratio |
chi2_ms(0) | 0.000 model vs. saturated
p > chi2 | .
chi2_bs(11) | 86.468 baseline vs. saturated
p > chi2 | 0.000

To see what is happening, run a simple regression model corresponding to your SEM and compare the results. I''m not sure of what you want to accomplish here but given the model you have shown us you don't really need SEM.

[Marcos Almeida]

Aside from all previous insightful advices, I fear that the variable "sanct", being a 6-level Likert scale, may not perform great under the proposed - sem - model.