# MPLUS - Modeling and SMS. 2. Create the statements for the mode...

## Question

MPLUS - Modeling and SMS.

2. Create the statements for the model in Figure 1 in the manuscript in Mplus and run the model. Then answer the following questions:
a. Interpret the Chi-square fit statistic and indicate what conclusion you would reach.
b. Interpret the RMSEA (including the confidence interval), the SRMR and CFI individually.
c. Write your conclusion on the overall model fit.
d. For any one of the unstandardized direct effects:
i. Write down both the null and alternative hypothesis, indicating whether the effect should be positive or negative.
ii. Indicate the value of the estimate, the standard error, test-statistic and p-value.
iii. Indicate the result of the hypothesis test, and your conclusion.
iv. Interpret each unstandardized coefficient.
e. Look at the standardized effects.
i. Interpret any one standardized coefficient.
ii. Indicate the R2 for each endogenous variable
iii. Comparing the standardized coefficients of the predictors, indicate which predictor has the greatest effect.
f. Estimate any one unstandardized indirect path from one of the exogenous variable to one of the endogenous variables, through a mediating variable an interpret it.
g. Look at the standardized coefficient of the path chosen in (f) and compare it with the standardized coefficient of the direct path between the exogenous and endogenous variable.
h. Compute the correlation residuals. What do they indicate?
i. Write a summary of the model weaknesses. In your answer, take into account the problems indicated by the global (overall) fit statistic and indices, the individual hypothesis tests of the path effects and whether the model is over-fitted based on the degrees of freedom and model.

3. Model Re-specification:
Your goal for the re-specified model should be a parsimonious model, where the following are satisfied:
1. The global model fit statistic and indices should be adequate
2. The path unstandardized path coefficients should be significant
3. All correlation residuals should be less than 0.1
You can begin by dropping non-significant paths in the original model, re-running it, and looking at the modification indices to further re-specify the model. You may have to do this iteratively a few times.
The more parsimonious your model that fits the data well, the better. But this does not rule out new paths (effects) being added to the model.

4. Final Model:
a) For your final model, repeat steps 2d through 2g.
b) Come up with one potential mediating hypothesis and test whether mediation is supported (Fully, partially or not at all)
c) For one change in the model from Figure 1 that you have implemented, provide a possible theoretical justification.

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2. Create the statements for the model in Figure 1 in the manuscript in Mplus and run the model. Then answer the following questions:
a. Interpret the Chi-square fit statistic and indicate what conclusion you would reach.
Chi-Square Test of Model Fit

Value                            16.229
Degrees of Freedom                     1
P-Value                           0.0001

Chi-square test of model fit value is 16.229. Since the chi-square test is significant (p=0.0001<0.01), the results suggest that the path model does not fit the data well.

b. Interpret the RMSEA (including the confidence interval), the SRMR and CFI individually.
RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.275
90 Percent C.I.                   0.168 0.399
Probability RMSEA <= .05          0.000

RMSEA values of 0.05 or lower indicate good model ﬁt, while RMSEA values of 0.06 to 0.08 indicate acceptable model ﬁt. Since the RMSEA value is 0.275 > 0.08, results indicate that there is not acceptable model fit. 90% confidence interval has an upper bound value of 0.399, which is above cutoff value of 0.06 (Hu & Bentler, 1999). Since RMSEA estimate and its upper bound CI value should both fall below 0.06 to ensure satisfactory model fit, our results show that the data does not fit model adequately.

CFI/TLI

CFI                               0.945
TLI                               0.508

CFI values range from 0 to 1. Higher CFI values indicate better model fit. According to Bentler (1990), a CFI value of 0.950 and higher indicate that the hypothesized model has acceptable fit. Since the CFI value in our example is 0.945 < 0.950, it means that our hypothesized model does not have acceptable fit. This is in line with the results obtained from Chi-square test of model fit.
According to Hu & Bentler (1999), TLI values of 0.950 and higher indicate acceptable model fit. Since the TLI value in our example is 0.508 < 0.950, the results indicate that model does not have acceptable model fit. the results are inline with the results of Chi-square test of model fit.

SRMR (Standardized Root Mean Square Residual)

Value                              0.048
A SRMR of 0.05 and smaller indicates that variances, covariances and means of
the model ﬁt the data well. Since the value of SRMR is 0.048 < 0.05 indicate that variances, covariances and means of the model ﬁt the data well.

c. Write your conclusion on the overall model fit.
The ﬁt indices indicate that the model does not ﬁt the data well: Chi square test is 16.229, p=0.001; RMSEA estimate...

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