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I am doing Exploratory Factor Analysis with 7 items. One of them (call it v1) have high correlations with 3 others, and other 3 are mutually moderately correlated. I tried extracting 2 and 3 factors, but multiple items have loadings on 2 factors.

If I remove v1, and extract 2 factors, then two items do not load highly on any of them. But 4 loads highly on factor1 and the last one loads highly on factor2. I am doing EFA to learn if there is any underlying concepts that give rise to the items (and not for just reducing the number of items), the two factors and the loadings of variables on them seem intuitive to me. But I am not sure if I can just remove an item. I saw this regarding PCA, and I understand the reason for not including collinear variables. But I need some reference to defend this in a paper I am writing.

My second concern is, the chi-square statistic is high and significant, meaning the model does not fit data well, no matter how many factors I extract (I cannot extract more than 4 with only 7 items). Is there any way to fit the model better?

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    $\begingroup$ Basically is similar to the discussion around outlier removal, it depends on your objectives and you need to take it into account when inferring anything. In the linked answer whuber stated 'There is nothing mathematically right (or wrong) about such a procedure; it's a judgment call based on the analytical objectives and knowledge of the data'. If your current aim is understanding underlying concepts, then you need to infer based on the original first. Then a separate analysis of whether there is benefit to removing colinear variables. $\endgroup$ – ReneBt Mar 27 '19 at 4:36
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Can you provide the output and code that you are using for your EFA? It'll be helpful in understanding your questions better. Some follow up questions: 1. How highly correlated are the four variables? 2. What method of factor rotation did you use? 3. Have you looked at some factor retention methods such as scree plot, parallel analysis etc.?

Chi-square statistics is not the best metric to guide you about your model fit. Infact some people caution against using only model fit indices to decide the number of factors in EFA (see Clark and Bowles, 2018, multivariate behavioural research)

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