Question

If I performed a confirmatory factor analysis (CFA), and these were my results:
(χ 2 (df = 289) = 689.66, CFI = 0.85, RMSEA = 0.054 (CI=0.049–0.059), SRMR = 0.067)
(χ 2 (df = 77) = 522.77, CFI = 0.90, RMSEA = 0.084 (CI = 0.077–0.091), SRMR = 0.050).

Is my instrument valid? If so, how?

Answer 1

(χ 2 (df = 289) = 689.66, CFI = 0.85, RMSEA = 0.054 (CI=0.049–0.059), SRMR = 0.067)

Here χ 2/df=689.66/289
  
=2.3864
  
we know that χ 2/df=2.3864 < 3 SO,it is Good.

Comparative fit index (CFI) :

Given the value of CFI is 0.85

Therefore it is considered very good if it is equal to or greater than 0.95, good between 0.9 and 0.95, suffering between 0.8 and 0.9 and bad if it is less than 0.8

So CFI value lies between 0.8 and 0.9 (0.85) So,it is Suffering.

Root Mean Square Error of Approximation (RMSEA):

Given the value of RMSEA is 0.054

Therefore it is considered good because it lies between 0.05 and 0.08

Standardized Root Mean Square Residual(SRMR):

Given the value of SRMR is 0.067

Therefore it is considered good because it's value less than <0.08

* The p value is significant in most cases. Therefore, it is suggested to consider the value of chi square / df instead of p value.

* So based on these values given,It is considered good fit i.e.. It is Valid instrument.

(χ 2 (df = 77) = 522.77, CFI = 0.90, RMSEA = 0.084 (CI = 0.077–0.091), SRMR = 0.050).

Here χ 2/df=522.77/77
  
=6.7892
  
we know that χ 2/df=6.7892 > 5 SO,it is not Good fit.

Comparative fit index (CFI) :

Given the value of CFI is 0.90

Therefore it is considered very good if it is equal to or greater than 0.95, good between 0.9 and 0.95, suffering between 0.8 and 0.9 and bad if it is less than 0.8

So CFI value lies between 0.9 and 0.95 (0.9) So,it is Good.

Root Mean Square Error of Approximation (RMSEA):

Given the value of RMSEA is 0.084

Therefore it is considered Suffering because its value >0.08

Standardized Root Mean Square Residual(SRMR):

Given the value of SRMR is 0.050

Therefore it is considered good because it's value less than <0.08

* The p value is significant in most cases. Therefore, it is suggested to consider the value of chi square / df instead of p value.

* So based on these values given,It is considered Bad fit i.e.. It is Invalid instrument.