Specific Question:
After went though the paper Basic Concepts and Procedures of Confirmatory Factor Analysis on the class web page several times, I got following questions.
① It say in the first part (Confirmatory Factor Analysis): Factor analysis is a generic term that we use to describe a number of methods designed to analyze interrelationships within a set of variables or objects…
In class until now, we covered two different factor analysis methods: EFA&CFA. I thought there were only two methods about factor analysis before. However, after read “a number of methods” in the paper, I used Google to search other methods and found no answers about the other methods. I am curious if there are some other factor analysis methods.
② It says (in Exploratory Factor Analysis part): The determination as to which form to use in an analysis is made based on the purpose of the data analysis. Exploratory factor analysis is used to explore data to determine the number or the nature of factors that account for the covariation between variables when the researcher does not have, a priori, sufficient evidence to form a hypothesis about the number of factors underlying the data. Therefore, exploratory factor analysis is generally thought of as more of a theory-generating procedure as opposed to a theory-testing procedure.I know that when performing EFA by SAS, we can use PC model as default to get the number of factors that SAS will give us. But, if we use ML method, we need to set the number of factors by ourselves. So, can I conclude that when we believe that there are 3 factors for example, and the correlations of the factors are not clear, we can use both EFA-ML and CFA and then use the fit statistic to choose the better fit one?③ It says (in Criticisms of exploratory factor analysis part): In a practical sense, there is no question that exploratory factor analysis serves a useful purpose in suggesting hypotheses for further research.Here, does the “suggesting hypotheses” mean the number of factors we can get from the EFA model?④ It says (in Confirmatory Factor Analysis part): In addition, confirmatory factor analysis offers the researcher a more viable method for evaluating construct validity. The researcher is able to explicitly test hypotheses concerning the factor structure of the data due to having the predetermined model specifying the number and composition of the factors.My understanding of this sentence is: we can use the fit statistics to test if the predetermined model we set is good fitted. Am I right? ⑤ It says (in Interpreting Confirmatory Factor Analyses part): It is important to remember when interpreting the findings from a confirmatory factor analysis that more than one model can be determined that will adequately fit the data.Dose it mean we may assume many different models by using different number and composition of the factors, and we may find that the results of these models are all good?? If my understanding is right, then does it also mean the hypothesis prior to the CFA is not unique?
General Question:
I read a paper about model fit indices online.
http://eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/16/cc/b3.pdf
The paper reviews the most frequently used structural equation modeling (SEM) fit statistics including chi squared, goodness of fit (GFI) and adjusted goodness of fit (AGFI) indices etc.
I have some questions about the model fit indices related to this paper. The paper holds that Chi-squared is the conventional overall test of fit in structure equation modeling. However, one of the main shortcomings of Chi-squared test is that the chi-squared test may not be a good enough guide to model adequacy when the sample size is small or big (Page6-7). I understand that this when the sample size is small, but can’t understand when the sample size is big. I though the larger the sample size, the better the test is.
The paper maintains that GFI and AGFI have the benefit of being more specific indices of fit than chi-squared statistics and they take degrees of freedom into account and eliminate some of the problems inherent in the chi-squared statistics alone (Page7-8). I am not clear about the GIF and AGIF here. What are the null hypotheses of GFI and AGFI in this paper, or saying GFI and AGFI in the structure equation models? Are they the same as those in chi-squared test?
The paper also supports that the root mean squared error of approximation (RMSEA) is one of most recently proposed tests of model fit and has been seen as a better indicator of fit than root mean square residual (RMR). And RMSEA is less affected by sample size, unlike the chi-squared statistics. I then run the SAS Job Satisfaction example we went through on Thursday again, finding that the RMSEA= 0.0975 with uncorrelated factors and RMSEA=0.0762 with correlated factor which means the second model is “fair fit”. I do not see the difference between RMSEA and RMR, RMSEA and GFI/AGFI actually, but based on the emphasis of the importance of RMR you made in class, I believe that RMSEA and RMR can be the most important fit statistics in our class. But in reality, we may refer to different fit statistics depending on different cases and models. Right?