# FACTOR SCORES IN FACTOR ANALYSIS

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• #2641

What is the use of factor scores in factor analysis?

I have done a factor analysis as a data reduction technique to identify the causes of mortality among aquaculture species. The factor analysis helped me to reduce the ten items into three factors with sufficient loadings.  The data has been collected from three districts.

Is it possible to use the factor scores to identify the prominent cause of mortality in each district?

Anyone who is well aware of this technique may please be reply….

Regards

#2649
Anonymous
Inactive

in order for you to do that, you’d need to fit multiple-group factor analysis to either test the invariance of the cause of mortality per district or, if you violate the invariance, estimate the factorial structure for the three separate districts. if you pulled the data from all three districts into one dataset it’d wash away any variance due to district membership…

#2648

Thank you for your reply.By estimating factorial structure for the three seperate districts, i could get factor scores in each district. But from the scores how can I identify a particular factor is the most important one causing mortality of species?

#2647
Anonymous
Inactive

hello there. multiple-group or multi-group factor analysis is not the same thing as running three separate factor analyses in three separate districts. a very good introduction to this method can be found in Basilevsky’s “Statistical Factor Analysis and Related Methods”. the thing is that, as i’m sure you know, a lot of the characteristics from a factor analysis solution is arbitrary. you can rotate those three vectors in infinite ways and get a solution with the exact same fit every time (a problem known in psychometrics as “factor indeterminacy”). for example, if you were to label Factor 1 as “the most important one” for District 1 and Factor 2 as “the most important one” for District 2, i could rotate the Factor from District 2 until it becomes as “important” as the Factor for District 1. you need the factor solution for the three districts to exist in the same factorial space to make it comparable and, ideally, find that there is invariance among those three districts to be able to make comparisons across them.

with that being said, we move on to issue #2 which is the concept of importance. Importance is not a statistical property of any method, but something people choose to evaluate. what does importance mean to you? does it mean accuracy of prediction? does it mean proportion of explained variance? does it mean appropriate model-to-data fit? different ways of defining importance may or may not give you different solutions so it’s kind of necessary to have a more precise definition of it…

#2646

Thank you oscar . First of all let me make it clear the details of my problem. Around 12 items were identified as the causes of mortality among the species cultured. The 300 sample farmers located in three districts of Kerala are asked to rate them on a seven point scale Very low……………Very high.From the data set using SPSS  I have done factor analysis which reduced the data into three factors Viz. Stocking problems,Climatic Changes and Natural disturbances.  Now, let me state my question once again

1. Using factor scores can I locate the most serious problem causing mortality of species from the three factors identified

2. Is there any difference in these three factors causing mortality across the districts selected

3. Which is the prominent cause of mortality of species in each district.

Let me reveal that I am not much aware about the technique multi- group factoring which you suggested as the best method for solving problem. I hope that your reference will help me to get insight into the technique.

Can you suggest  some simple methods to solve the problem using SPSS?

Once again thank you for answering my simple queries….

#2645
Anonymous
Inactive

not a problem, i am glad i can help…

i am having a little bit of trouble seeing how you’d be able to locate the seriousness of the cause of morality from factor scores, given that there are many ways to obtain factor scores (i’m an R user, not an SPSS user so i’m unaware of which particular method is implemented by SPSS, although i think it would be a safe bet so say it’s just doing a linear regression). now, you said that from your factor analysis you obtained three factors. may i ask a) how did you decide on choosing 3 factors instead of 2 or 1 or 4?  and b) did you rotate such factors?

words like prominent cause of mortality or serious problem are very difficult for me to conceptualize because, as i mentioned on my previous post, they have no mathematical meaning and different people would call different things “prominent” or “serious”. i’d need to reiterate my question… what is the ultimate goal of your analysis? prediction? explanation/accounting of variance? hypothesized model-fitting? i need to be able to quantify “prominence” or “seriousness” somehow to answer that, and the only way i can do that is if i know what exactly you’re looking for. do you have a research hypothesis? that should provide the guidance needed to determine what is “prominent” or “seriousness”.

i’m not sure whether you did this inadvertedly or not, but yours is actually not a very elementary design. it is doable, but is certainly beyond the capabilities of your standard SPSS-like analysis. the question of invariance of factorial structures across groups (districts in your case) is not particularly straightforward because the sampling distribution of the eigenvalues from a correlation matrix is not known. it is, to the best of my knowledge then, impossible to perform something akin to a two-sample t-test between factors to decide statistically whether factors are different across districts. besides, how do you know that a three-factor solution holds in each district? how do you know district 1 has three factors, district 2 only has two and district 3 has only 1? you can test this via multi-group factor analysis but it is not immediatley apparent to me how you can do that just by conducting a simple exploratory factor anlysis.

i think you may actually need an expert that can provide you with step-by-step guidance along the way if you haven’t done this before… i cannot really help out much (aside from just giving you some general guidance) without actually sitting there right next to you and ask you questions, look at the data, guide you through the analysis process, etc.

#2644

to make my doubt more clear let me say something more. In my study relating to production and marketing of aquaculture products in kerala, One variable I have used in connection with production is causes for mortality of species. The 12 items used as causes of mortality is reduced to three factors after checking correlation,communalities, eigenvalues and factor loadings from rotated component matrix using SPSS. Now I am looking for further analysis.

So the question is can I use factor scores for further analysis especially for prediction.

The three factor solution I have developed is for the whole data. A district-wise factorial design may give yet another list of factors.

Now I need your expert advice is to suggest some methods that can be used for further analysis after deciding factors.

Hope I am not causing much trouble to you.

Thank you Oscar.

#2643
Anonymous
Inactive

now that you’ve shared more information with regards to your study design, i am beginning to see that there is somewhat of a disconnection between what you’d like to know and your analysis of the data. your factor analysis is on the ratings from the farmers and not on the actual variables that you believe are related as causes of mortality in aquatic species. for instance, factor scores in this case would only be able to tell you where are thefarmers’s perceptions of causes of mortality in the latent variable/factor continuum, but that won’t tell you anything about the real causes of mortality.

i was under the assumption that you had made your readings on the actual variables that you considered may be causes of mortality (variables such as, i dont know, acidity of the water, level of pollution, density of chemicals on the water… i mean, i am not an expert on this field so i am just throwing ideas around) but now i realize the readings are on the farmers. so any kind of conclusions you can derive from this analysis is not in the causes of mortality but what the farmers think are the causes of mortality, which may or may not represent the real causes because different farmers are affected differently by different causes.

so what you are interested then is not on predicting causes of mortality but what farmers think are causes of mortality… am i correct? because if not, then you should not be doing a factor analysis on the farmers ratings but on something else (or probably not even a factor analysis at all).

it seems like the more you reveal about your study the more i realize you need to actually work with someone who can guide you with this process because now i see multiple-group factor analysis may not even give you any information about what you’re looking for…

#2642

this is exactly what i meant. The factor analysis i have done is based on the farmer’s perceptions of causes of mortality which is given as 12 items on a seven point scale. Let me reveal that i am not a scientist but belong to social science stream (Commerce). the basic emphasis given on my study is production and marketing of aquaculture species in Kerala. Actually I have done factor analysis on these 12 items used for rating farmers perceptions regarding causes of mortality which lead to the identification of three factors in total. Does it mean that factor analysis is not the suitable tool for this variable?

Thank you Oscar for the valuable time you spared for me in answering my basic questions…..

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