Selecting a Rotation in a Factor Analysis using SPSS

hello this is dr. Grande welcome to my video on selecting a rotation method in a factor analysis in SPSS oftentimes in counseling research we want to reduce a number of items for example from a psychometric test into clearly defined factors and we use factor analysis to accomplish this goal and part of identifying and defining factors is to use was referred to as a rotation so first let's take a look at these fictitious data I have in the SPSS statistics data editor you can see have 10 variables item 1 item 2 all the way through item 10 and the values in each cell in each record range between 1 and 5 so if you see here for record 1 item 1 as a 5 item 2 is a 1 item 3 as a 4 and so on and we could think of these as responses to an individual item on a psychometric assessment perhaps a Likert scale where one represents strongly disagree and 5 represents strongly agree so to get started with selecting a rotation method I'm going to start the factor analysis procedure for these 10 items so I'm going to go to analyze dimension reduction factor and this is what the factor analysis dialog looks like by default over here in the list box on the left I'm going to hit ctrl a and select items 1 through 10 and move them over to the variables list box of interest here of course is the rotation button I take a look at these other options first under descriptives I'm just going to add coefficients determinate and kmo and Bartlett's test of sphericity and the univariate descriptive as well under extraction I'm just going to add these scree plot I'm gonna make no other changes here underscores there'll be no changes and under options I'm going to under this frame coefficient display format I'm going to change this to sorted by size this is an important checkbox sorted by size and then continue and now let's take a look under rotation so we can see under the method here you can have no rotation you can have ver max quarter max or equal max these three methods are called orthogonal rotations and we use these when we believe that the factors that we're going to be extracting are uncorrelated and then you have direct of lemon and Promax and these are considered oblique rotations and we would use these when the factors are correlated so before I start the process of selecting a rotation want to explain what a rotation is we can think of a rotation and a factor analysis as a mathematical procedure that rotates the factor axes in order to produce results that are more interpretable so it makes the loading patterns more clear easier to identify more pronounced the whole purpose of rotation is to create what's called the simple structure and the simple structure if it's achieved through rotation will be easy to interpret so that's the goal so the global rotation is to obtain a simple structure that can be interpreted so that we can make sense of the factor loadings so how do we go about in selecting a rotation method as I mentioned we have vert max quarter Max and equi max and we assume here for these three rotations that the factors in the analysis are uncorrelated and direct of lemon and Promax or oblique rotations and we assume for these the factors are correlated so first we need to determine if the factors are uncorrelated or correlated so we know if we would select an orthogonal method or an oblique method orthogonal rotation or oblique rotation so first I'm going to go to direct o blimmin which is an oblique rotation method and I'm just going to leave display set to rotated solution and leave the maximum iterations for convergence set to 25 click continue and then click OK now we have a lot of output that's generated here by SPSS in this example but for the purposes of this video I'm just trying to determine what rotation would be the most useful for us given this particular set of data so here I'm going to move down all the way to the end of this output I'm looking for the component correlation matrix and what I'm looking for here specifically in the component correlation matrix is any correlation between the factors or components that is greater than 0.32 or less than negative 0.32 so another way of considering this would be we're looking for any value here that if we take the absolute value we have exceeded 0.32 now of course we're going to exclude the components correlation with itself that's always going to be one so you can see we have the ones that run diagonally we're going to exclude those and if we take a look at the other values we can see here there's no other values if we take the absolute value it would exceed 0.32 if we did have a value that exceeded 0.32 we would use an oblique rotation so that would be either direct of lemon or Promax either one of those rotations would work in that case in this case since none of the absolute values exceed 0.32 we're going to use an orthogonal rotation so I'm going to go back to analyze dimension reduction factor and this is going to save all the settings from the previous factor analysis so I just need to go into rotation and for the orthogonal rotation methods I have the choice of Vera max Core Max or equal max I'm going to use the Vera max so I'm just going to change from direct OBE lemon - Vera max and click continue and then click ok so again there is a significant quantity of help put here so I'm going to move down to the rotated component matrix that's what I'm interested in the rotated component matrix and I'm going to be examining this matrix to see if it qualifies as having a simple structure now there are a great variety of definitions for simple structure but in general there's just a few things that we're looking for here what we like to see is for example here with component 1 and item 10 item 8 we want to see significant loadings on one component in this case we have 0.83 for item 10 and 0.788 for item 8 and then we want to see as many zero loadings for the other components as possible knowing that we're not going to have entirely zero components in most cases now a zero component can be roughly defined as any factor loading that is greater than negative 0.1 and less than 0.1 we also want to keep an eye out for significant loadings and again there are many opinions about what's a significant loading and what is not a significant loading any loading greater than 0.3 could be considered significant but it's not unusual for researchers to use 0.4 or 0.45 and at the same time we want to be on the lookout for complex variables in this case our variables are items so we be looking for items that have a loading of 0.3 or greater on two or more factors that would be a complex variable so with those guidelines in mind let's take a look at the rotated component matrix and you can see here if we look at item 10 item 8 again they have strong loadings so they they seem to be loading together they seem to represent a component and we can see we have zero loadings here on component to zero loading here on component three for item eight but not for item ten and the same result for component for a zero loading Friday mate but not freedom ten but neither one of these items represe a complex variable because we have a significant loading here for component 1 but no other significant loadings no other factor loadings that exceed 0.3 so now let's move to component 2 and we can see we have strong factor loadings here for item 5 and item 6 so they appear to be holding together as a factor and we have several 0 loadings but then we have a few instances where we do not have 0 loadings here at 0.15 4 and component 3 5 and 5 and again for component 1 on item 6 0.21 then moving on to component 3 we can see the component 3 appears to have item 1 item 2 an item nine point eight three six point seven two five and point four six nine we only have one zero loading for item one and that's a component two and we have two that violate the zero loading rule so they do not count as zero loadings for item two we have two zero loadings but then we have for component 1 a factor loading of 0.3 0 2 so this means that item 2 is a complex variable it has a factor loading of 0.7 to 5 on compounded 3 and point 3 0 2 on component 1 and then for item 9 again we have 0.469 for component 3 to 0 loadings and then a not zero loading on Copiah - of 0.1 for 6 and again for the last component we just follow the same process we can see we have 2 0 loading striving for one nonzero loading for item 3 we have a non zero loading here negative 1 point 3 5 and we also have a value of point three seven one so again item 3 is going to be another complex variable then we have a zero loading and of course the point six four nine which we would consider to be indicative of where this item loads so we believe that item four three and seven all load on factor four and then for item seven we have two non zero loadings here and then one zero loading Oh point zero nine three and then 0.59 five and again we believe these are grouped together so four three and seven appear to be grouped together on factor for item one item to an item nine appear to be grouped together on factor three item five and six appear to be grouped together on factor 2 and item items ten and eight appear to be grouped together on factor one so this is with a varimax rotation so if we went back in to analyze dimension reduction factor and switch this rotation to another orthogonal rotation let's go with Quarter Max and click continue and then okay I'm going to take the table we were just looking at which is the rotated component matrix so we can see in this last factor now so so a quarter max we can see the rotated component matrix so I'm going to take the rotated component matrix and the other analysis and kind of move that down a bit and here you see we have the rotated component matrix that I was just looking at the Vera max and now we have the quarter max so we can compare them one on top of the other and we can see that the results are very close items ten and eight are together here items five and six are together here for factor three we have items one two and nine just as we would with the Vera max and then items four three and seven hold together and again the factor loadings in the quarter max rotated component matrix or identical or very close - the factor loadings in the varimax rotation in the rotated component matrix for the varimax rotation so let's go back in and take a look at the last orthogonal rotation and that would be the Aqua Max and again I'm going to range this output so we can see these tables near one another so I've arranged it so the Vera max is on top then we have quarter Max and then aqua max here at the end and again you can see all the values are either identical or very close with the Aqua Max rotation to the factor loadings that we see in the quarter Max and the Vera max rotations and the conclusions we would draw would be the same items ten and eight together five and six together one two and nine together and four three and seven appear to load together now in terms of which rotation you want to interpret or which rotation you want to use to assist in the interpretation of the factor analysis in this case these are pretty close to the same for this particular fictitious data set there's really not much difference between any of the orthogonal rotations if there were a difference between them of any note you'd want to select the rotation that brought you the closest to the simple structure so again you'll be looking for the rotation has the fewest number of complex variables or no complex variables and for the rotation that provided zero loadings on factors where there was not a significant loading I hope you found this video on selecting rotation for a factor analysis in SPSS to be useful as always if you have any questions or concerns feel free to contact me I'll be happy to assist you

Channel: Dr. Todd Grande

Views: 37,171

Rating: 4.9108634 out of 5

Keywords: SPSS, factor analysis, rotation, rotations, rotated component matrix, simple structure, complex variable, factor loading, factor loadings, significant, zero loading, orthogonal, oblique, varimax, quartimax, equamax direct oblimin, promax, factor analysis tables, descriptive statistics, correlation matrix, component matrix, matrix, counseling, Grande

Id: nIv8h4rQ7K4

Length: 17min 12sec (1032 seconds)

Published: Wed Mar 02 2016