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 ï¬t, while RMSEA values of 0.06 to 0.08 indicate acceptable model ï¬t. 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 ï¬t the data well. Since the value of SRMR is 0.048 < 0.05 indicate that variances, covariances and means of the model ï¬t the data well.

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

Make a full regression predicting quality from density for all inte...