Exploratory Factor analysis, of which there are several variants.

If you are new to it, I recommend an excellent (albeit older/classic) text by Rummel on applied factor analysis.

The short version is: EFA refers to a variety of data reduction techniques that, through application of matrix algebra, identify common themes in items/indicators (e.g., survey items, although any data might be EFA'd). I recommend using a form of principal axis rather than principal components (they differ in regard to a few theoretical assumptions and computational methods), but either will move you towards the end of identifying, empirically, the "best" (i.e., most representative, non-redundant) items to assess a common underlying theme (depending on your theoretical orientation, that common theme corresponds to an underlying concept or construct, for which certain clusters of items are individual indicators, somewhat analogous to related but distinct symptoms of a given syndrome).

Anyway -- start with Rummel. A great introduction. His website has tons of useful info as well http://www.hawaii.edu/powerkills/DIMENSIONS.HTM

His particular subject interest is possibly quite different from your own, but the methods and principals of the analytic methods and their application can be applied to any problem where you have a large number of variables, and would like an empirical method of determining whether they might be reduced to a smaller set, organized on the basis of (ideally) an interpretable common theme or set of themes.

Hope that helps!

Exploratory Factor analysis, of which there are several variants.

If you are new to it, I recommend an excellent (albeit older/classic) text by Rummel on applied factor analysis.

The short version is: EFA refers to a variety of data reduction techniques that, through application of matrix algebra, identify common themes in items/indicators (e.g., survey items, although any data might be EFA'd). I recommend using a form of principal axis rather than principal components (they differ in regard to a few theoretical assumptions and computational methods), but either will move you towards the end of identifying, empirically, the "best" (i.e., most representative, non-redundant) items to assess a common underlying theme (depending on your theoretical orientation, that common theme corresponds to an underlying concept or construct, for which certain clusters of items are individual indicators, somewhat analogous to related but distinct symptoms of a given syndrome).

Anyway -- start with Rummel. A great introduction. His website has tons of useful info as well http://www.hawaii.edu/powerkills/DIMENSIONS.HTM

His particular subject interest is possibly quite different from your own, but the methods and principals of the analytic methods and their application can be applied to any problem where you have a large number of variables, and would like an empirical method of determining whether they might be reduced to a smaller set, organized on the basis of (ideally) an interpretable common theme or set of themes.

Hope that helps!

I agree with Jordan. On my side, you can do it by reducing lower loading items (normally below .5) after EFA (exploratory factor analysis). I know one simple book Julie Pallent's SPSS manual. hope this will help.

You can refine the questionnaire via face validity, which are done by a panel of experts about five experts and professors in field of your scope. They will check and edit your questionnaire before  analyzing. If your model is complex or have many constructs, you can use Amos to analyze. using multiple squared correlation and standardized residual error matrix are utilized to evaluate scales. you must use discriminate and convergent validity to evaluate scales as well.

There have been so many questions like this that I have started a thread that addresses these issues:

https://www.researchgate.net/post/How_can_one_help_people_create_simple_scales_from_Likert-scored_items

Two of the things that you will find there are resources with regard to both Cronbach's alpha and exploratory factor analysis.

it depends....

if they are reflective (mode A) or formative (mode b) item measures. You cannot reduce the measure from mode b as it assume your items captures the universe of the conceptual meaning for the defined construct.

see bollen and lennox (1991)

or also any Wynne chin article/chapter in the late 1990s

I would recommend never using cronbach's alpha. use maximised reliability. Werts, linn et al.

Cronbach's alpha is unitary weighted and as such is a lower bound estimate

regards

brad

Hi,

I would agree with Bradley that you first have to consider if the measures are reflections of a common cause (=factor) or *constitute* some kind aggregate/composite.

It is only the first version that forms the basis of the term "measurement".

If you have indicators of a common factor than avoid exploratory factor analysis and directly switch to confirmatory methods. You have an idea about the factor structure - why then delegate responsibility to an algorithm :)

You will then find (I guess) that the model won't fit because traditionally, scales were constructed using rather heterogenous sets of items. These, however, imply measures of different factors. Hence, you will have to respecifiy the structure and come along with a proposal of a "more-than-one-factor" model. This is the basis for your item selection:

a) for which of the factors do you actually want measures? (--> theoretical model)

b) which are the best items? (--> loading and plausibility)

Avoid such things as "covering breadth"-ideas when selecting items (remember, we're in the "reflective indicators" mode. If your construct is an aggregate construct, then ONLY select indicators that span the domain. In my point of view, however, such constructs and their scales are ontologically completely ambiguous.

Best,

Holger

A lot of the social sciences literature is littered with studies and articles that are misspecified in their choice of measurement orientation.

NOW... i decades past this may have been excused due to computational complexity, available computer processing power and just available software....

BUT modern researchers ... need to carefully consider such issues at the outset AND just because you are taking somebody else's scale or questionnaire items that have been published does not mean they did not do the wrong thing and get published. BEWARE and I encourage even junior researchers to question the so-called NORM.

Holger, add another dimension.... is your work to be framed at exploratory, alternative models, model generating OR strictly confirmatory (joreskog in SEM talks of these distinctions).

Unfortunately much publication bias exists and many academics frame their whole write up in terms of it be about one or two alternative model OR strictly confirmatory WHEN THE PROCESS AND LEVEL OF DEVELOPMENT IS TRULY EXPLORATORY and they do not write up that way.

better reviewers and editors will hopefully limit this publication bias moving forward.

you ask a simple question.. we give you such a scary response/s with so much to consider!

enjoy

Brad

You can use the exploratory factor analysis employing the Principal component analysis 

Factor Analysis

Hi guys,

please do not do (again) the mistake of equating factor analyis with principal component analyis. In the meantime there tons of articles bout the fundamental differences. Here are just a few...

Best,

Holger

Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift’s electric factor analysis machine. Understanding Statistics, 2, 13–43.

Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299.

Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110(2), 203–219.

Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5(2), 155–174.

Bandalos, D. L., & Boehm-Kaufman, M. R. (2009). Four common misconceptions in exploratory factor analysis. In C. E. Lance & R. J. Vandenberg (Eds.), Statistical and methodological myths and urban legends - Doctrine, verity and fable in the organizational and social sciences (pp. 61–87). New York: Routledge.

consider directionality of items AND then make analytical choices from there.

many responses miss the point I am making.

brad

I disagree about the idea of "never" using Chronbach's alpa for several reasons. First, you should look at the standards within your own field and pursue your analysis accordingly. In some field's, Cronbach's alpha is considered to be a kind of gold standard, and if you don't report it, your reviewers will criticize you.

Second, in terms of creating scales that you can actually use, simply summing up the items has a lot more integrity than the indeterminacy of getting weights for factor scores. In essence, using factor scores to create scales has been replaced by Structural Equation Modeling, but that approach is not for beginners.

Finally, in terms of the supposed limitation of giving the items unit weights, it turns out in practice that you need a lot of variance in your factor loadings before this makes a substantial difference. And if you doubt that, try calculating two versions of a scale, one by just adding the items and another by using factor scores, and then correlate the two.

Dear David,

if you allow me some comments - just as an add on (capitals are only used to stress terms):

a) Cronbachs alpha is a measure of reliability IF essential tau-equivalence holds - that is all items measure the same underlying factor AND the factor loadings are equal. If these assumptions fail, you will get a low alpha but that does not mean that the reliability is low.

Alpha is not suited for adressing issues of uni-dimensionality (see below). I agree that it is wise to follow standards - but at the same time, wrong standards can only change if someone starts not repeating things that have been simply copied a thousand times. 

b) Summing up items REQUIRES that the factor model is valid. Hence, it should be tested. In structural equation modeling (SEM), item parceling (summing without testing) is harshely criticised. I agree however, on the problems of using factor scores. Hence, I vote for fully go to SEM with latent variables. I again agree that summing items reduces random errors (again - if the model is correct) but clarifying the structure (and testing it) is - in my point of view - more transparent. 

All of this requires that you have a factor model in mind (that is, you imaging an existing entity that causes a bunch of indicators). If you have, however, an aggregate construct in mind (e.g., an index) you can do whatever you want. Applying terms like "measurement", "truth" and "validity" is not suited here (see the paper by Denny Borsboom about the ontological status of latent variables versus indices/formative models that I posted). Further, calculating alpha gives totally wrong impression about reliability (sometimes alpha may be 0 or even negative and means nothing). 

As aforementioned, my comments are based on the full respect of your work and your above stated points.

With warm regards,

Holger

Additionally, I also suggest to conduct a pilot among potential interviewed. Some questions may be difficult to understand and answer and some may be not focused on the experience of your population target.

Anna M.

Hall sir, I would like to share my views on said question. you can use this formula for reducing the large number into small no.

                           N

                    -----------------

                       1+n(e)2

Taro, Yamane, (1970), “Statistics: An Introductory Analysis”, (2nd Ed.), Harper and Row, New York pp.886-87

standards and publishing conventions are sometimes misguided. Holger is right on tau equivalence.

see work of tenko raykov.

AND people have forgotten the scenario of Mode C measurement where there is a mixture of formative and reflective items representing the construct.

good debate.

brad

Holger,

I wish everyone had the skills to do Structural Equation Modeling. There is no doubt that building and testing a measurement model is superior to the simplistic assumptions behind Cronbach's alpha.

Having said that however, I think it is important to recognize that many beginners in this area are not just unaware of Confirmatory Factor Analysis but also totally lacking the instructional resources to acquire that skill.

So my approach is to "light a candle rather than curse the darkness" by giving beginners a place to begin.

Quick follow-up comment regarding alpha -- great paper on the SE of alpha here http://resource.owen.vanderbilt.edu/facultyadmin/data/research/2389full.pdf

Also, alpha tends to be inflated with a large number of items and underestimates internal consistency when the scale is brief. Looking at other indices, such as mean inter-item correlation, is very informative, especially for a scale with only a few items.

I would push my students... Even honours ones through sem.. Cbsem or pls.

I think we need to be teaching latest advantageous techniques if possible.

we definitely need to be publishing with them.

BUT I do understand we need to walk before running.

brad

Hey Bradley,

Nice words (although I'd strongly disagree about using PLS ;) but that's a different story :)

Best,

Holger

EFA is a good solution for data reduction.The items that share common characteristics are brought under one factor which may further be analysed.

Dear Uma

1) Did you read the postings in this thread? As I think, there were some discusions referring to EFA

2) "share a common characteristics" is a rather weak interpretation of the factor model (which the ...FA (C or E) implies. The factor model is a causal model that posits that a bunch of item share a common cause - not characteristic. Hence, inspection of factor solutions either in a EFA or CFA should be guided by this essential issue: "it is reasonable that this bunch of items are influenced by the same underlying thing".

Best,

Holger

See new MISQ .... new PLS algorithm that has very beneficial qualities.

enjoy the reading

brad

I think most of the responses given are addressing the question after data collection. I think the question is before data collection where the researcher feels the questionnaire is too long. 

In response I would suggest a qualitative approach where you need to identify your main Objective of the study. Then split your main objective into more specific objectives that when addressed individually you can still get the right answers for your study. You continue splitting until you get to a point where the size of your questionnaire is just right. In the process you will realize that there are other questions you can join into one without loosing meaning and value . example instead of asking four questions about, age, gender, profession, qualification  you can just say tell us about yourself regarding age, gender, profession and qualifications and give space . Serious respondents will give you all you need to know sometimes even more like race, marital status, employment status etc   

Besides quantitative techniques already presented, qualitative methods may be used to reduce the number of questions, without sacrificing quality of results.

1. Always have in mind the general and specific objectives of the research: confronting them with the question, you can see if it is really necessary. If it does not contribute to the general or to specific, should be discarded.

2 Transform questions in responses. Por example, instead of asking the owners of vehicles in individual questions if economy, comfort, performance, price, autonomy, are important when buying a car decision, you can use just one question: which of the following items are most important in the purchase decision of a vehicle? Display with 1 the most important and 5 the least important. (See Boyd & Westall, Marketing Research,chapter 7)

3. You can also transform questionnaires in forms, more concise and easy to fill out. (Pizzinatto et al, Marketing focused on customer chain, Chapter 6, by Maris de Cassia Ribeiro)

Exploratory Factor analysis 

To answer your question we need to know the purpose of the study. If the purpose of the study is to develop a new scale, then the process is time consuming, and the reduction of questions needs to follow a specific process. I have included some references;

Gerbing, D. W., & Anderson, J. C. (1988). An updated paradigm for scale development incorporating unidimensionality and its assessment. Journal of Marketing Research, 25(2), 186-192.

Rossiter, J. R. (2002). The C-OAR-SE procedure for scale development in marketing. International Journal of Research in Marketing, 19(4), 305-335.

DeVellis, R. F. (2003). Scale development: Theory and applications (2 ed. Vol. 26). Thousand Oaks, CA: Sage Publications.

If however, you do not want to develop a new scale than the processes outlined in the previous responses should help you reduce the number of questions. Focus on the primary purpose and objectives of the study.

Reducing the number of items...

a) ... before you applied the questionnaire in a sample? Then use theoretical considerations or cognitive interviews (Willis GB 2005).

b) ... after having applied the questionnaire in a sample? Then you can use the data to calculate psychometric parameters for each item (the "reliability analysis" in SPSS) in order to choose the best items in psychometric terms. These parameters are primarily: item difficulty, item discriminability or the combination of both, called the selection index. For example, we have omitted all items with a selection index below 0.25 in one publication.

In my view, methods like PCA, factor analysis, SEM, cluster analysis are analytic methods to simplify the data structure for a better interpretation. Before that, you have to do the psychometric analyses as described.

You can use factor analysis to reduce the factors to a manageable size

You can use Exploratory Factor Analysis. 

Kindly refer to the following article for more details:

http://www.let.rug.nl/nerbonne/teach/rema-stats-meth-seminar/Factor-Analysis-Kootstra-04.PDF

If you are using SPSS for your Data Analysis then you can watch this video to know about the procedures

http://www.youtube.com/watch?v=-6tw7ebr860

Of course,there are certain guidelines available in books related to research in general and Research methods ,in particular i-e Self-critique,External scrutiny,Pre test and pilot study etc.If your sub construct and indicators are clearly defined this can also help to stay inside certain limits even at the initial stage i-e constructing questionnaire.I would recomend you to read "social Research Methods" by Soitirious Sarantakos.Good luck

I would suggest you to read "Social Research Methods" by Soitirious Sarantakos .Hopefully it will help you a lot.

Hi everyone, I have a doubt on formative and reflective indicators.

In general scale development process, we use principal component analysis to extract factors and the output also contains component or factor scores. This approach indicates that all the items on a component (factor) are contributing to it rather than reflecting it, making the indicators formative in nature. Is not it? and then the process includes CFA and validity, reliability test that does not go well with formative indicators.

Hi Swati Hans

exactly, you summarized decades of problematic procedures in a few sentences :)

Best,

Holger

Hi Mr. Holger,

If this is the case, then the scale development process includes a step relevant for formative indicators (PCA) and another step relevant for reflective indicators (CFA, validity, reliability) and finally, we conclude the indicators to be reflective (in most of the scales). So, what is the nature of those indicators? I am damn confused now.

Hi,

from an epistemological perspective, reflective factor models have a strong advantage against so-called formative indicators: The make a statement about some underlying existing data generating process and an existing entity that drives this process. These statements are testable (in a CFA or better, a full SEM).

Formative indicators or aggregate constructs are, first of all, lists of facets meshed together and have no existence beyond this meshing-process (see Borsboom et al., 2003; Lee/Cadogan, 2016). Hence, there is nothing testable. PCA may be a method to approach these empirically but I don't think that it is necessary, as "inter-correlation" as an organizing principle (that underlies PCA) is just one of the possible. Others may be simply "accordance with some theoretically based inclusion criteria".

There are some folks (for instance) from the PLS field, that try to build some realism-based fundament for proposing formative indicators--namely as "contributing to some emergent construct" that would not exist without the presence of all of the indicators. An example could be "bread" that would not exist without the complex interplay of its ingredients. This is theoretically very nice and appealing, although I think that it is analytically very complicated. In the moment, they use this idea as a theoretical basis for simply adding formative indicators together which-in my point of view--does not quite match the proposed interactive interplay of the ingredients implied by the emergent process idea.

But I will follow the further development :)

Best,

Holger

Borsboom, D., Mellenbergh, G. J., & van Heerden, J. (2003). The theoretical status of latent variables. Psychological Review, 110(2), 203-219.

Lee, N., & Cadogan, J. (2016). Welcome to the desert of the real: reality, realism, measurement, and C-OAR-SE. European Journal of Marketing, 50(11), 1959-1968.

The EFA exploratory factor analysis is used to reduce the factors in a scale which hasn’t many items.after the efa we take the items whcih have the maximum loading