Factor Analysis (Principal Components Analysis) with Varimax Rotation in SPSS

hello this is dr. grande welcome to my video on conducting a factor analysis with varimax rotation in SPSS I have here a fictitious data set with an ID number and ten items from an assessment so as opposed to some sort of scale score from the assessment these would be the actual responses given by the participant on each item of an assessment so this assessment has ten items and for participants a one zero zero three on item three the value they selected was 56 it's important to understand the data structure starting out with factor analysis because of what a factor analysis does which is to explore the underlying constructs in an assessment so as we're looking at this data and we're thinking about what type of statistics to subjected to and what we might do with the instrument in terms of development in the future we think of factor analysis as being able to tell us about the constructs that may exist that are revealed by these ten items so are there two constructs are there three constructs what does this particular assessment measure now a factor analysis will not tell us what the constructs are that has to be reasoned in a more qualitative way meaning look at looking at each item and subjectively to a degree assessing what construct it's tied to but a factor analysis will from a statistical point of view give us groupings that we can then look at so it'll tell us mathematically which items hold together which items appear to be measuring the same construct so before I start with the factor analysis I want to make an important note about the term factor analysis and the term principal components analysis the analysis I'll be running here is actually a principal components analysis that type of analysis is different than a factor analysis but often times the terms are used interchangeably so to conduct a factor analysis we'll first to go to analyze then dimension reduction then select factor and you can see I've already populated this variables list box with all the items which is how you want to be arranged so you don't want the ID number over there you just want the actual scores for each item the item variables in this case there are 10 and there's no selection variable for descriptives I have univariate the initial solution and for correlation matrix coefficients determinate and KML and Bartlett's test of sphericity for extraction you can see the method is principal components analyzed with the correlation matrix I want to display the unrotated factor solution and the scree plot and I want to extract based on an eigen value greater than 1 it's worth noting here that you do not have to allow SPSS to decide how many factors to extract you can select fixed factors that are fixed number of factors and simply input the number of factors you want to extract but that would usually be for later analysis let's look at just based on Augen value of greater than 1 click continue for that so for rotation there's two main types of rotations orthogonal and oblique and we would use orthogonal when we believe that the different variables are not correlated highly to one another and oblique when we believe they are correlated now in the social sciences such as in counseling oftentimes items that we have on assessments are highly related but for this example I'm going to presume that these items are not so we can use a varimax rotation which is the most popular orthogonal rotation I'm also going to display the rotated solution click continue here now under scores I'm not going to save the factor scores as a separate variable but it's important to know that you can do that and a popular method for doing this would be the Anderson Reuben method and then for options I'm going to exclude cases loose wise and I'm going to sort by size so the coefficient display format sort by size and click continue so now we're ready to run the analysis so I'll click OK and you can see there is quite a bit of output after running a factor analysis so let me go through what we have here first there are the descriptive statistics you have the means and standard deviations and the N for each of the 10 items so you can see there's no missing items here and you can see there is there are differences rather between the means of these items and there are differences in the standard deviations then we have the correlation matrix now what's really looking for here is a value of less than negative 0.8 or greater than 0.8 so a correlations stronger than 0.8 would be a red flag clearly as you can see because this is a matrix item one is going to be perfectly correlated with item 1 & 2 a2 and so on that creates that diagonal there of ones of course is the other values that we're concerned with and as we look through we see a few like item 5 9 to 0.32 7 but still very far away from 0.8 so nothing on here really raises any red flags guarding the correlation and in terms of the determinant value you can see down here a determinant equals 0.48 2 really what you're looking for there is any value greater than point zero zero zero zero one so 0.48 2 is certainly in the safe range they're moving down to kmo and Bartlett's test we have a value here of 0.5 1 9 and we're looking for value of greater than 0.5 so that is greater than 0.5 but it's it's not ideal it's very close to 0.5 and for significance in this case we do want statistical significance and point 0 1 2 is statistically significant it's worth noting here on the kmo and Bartlett's test as I mentioned 0.5 1 9 is very close to 0.5 0.5 is really the the absolute minimum and ideally this value should really be above 0.9 or 0.8 but technically speaking anything above the 0.5 is acceptable similarly the significance level here is technically acceptable but point 0 0 1 would be a lot more desirable significance level so moving down to total variance explained so as you can see here has five components that explain 66% of the variance so the results of this factor analysis indicate there are five components explaining 66% variants and you can see that on the screen here's the eigenvalue of one you can see that there's five components that have an eigenvalue greater than 1 so the results indicate there are five distinct constructs in this instrument of just 10 items as we move down we have the component matrix but I'm going to move to the rotated component matrix and you remember I had this sorted by size and here here's that feature really pays off so you can see here here are the five constructs or components that the factor analysis has identified and you can see that in for the first component item four and item one load together pretty well Oh point seven five eight and point seven five and then moving to component two you can see that items five and two load together pretty well so it's like a stair-step effect here when you have it sorted by size and then moving to item three eight and ten tend to load together pretty well and then moving down to item four a little trickier but you have six three and nine those items tend to load together fairly well but on item five item nine or component five item nine and item seven load together relatively well but the strengths here like item nine is a better fit for fact the construct for component 4 than it is for the fifth component now as I'm looking at these values this does appear to be kind of weak value compared to the others right item nine doesn't quite fit in as well as some of the other items here it has a low factor loading of just 0.4 one so let's move back to the data set and run the analysis again except this time I'm going to remove item 9 so if you're designing an instrument this is one way you could do it so I'm going to click OK so the same analysis everything else is the same except now I've removed item 9 for the analysis and let's see how this impacts the results the correlation matrix still looks pretty good no values greater than 0.8 the kmo is still really close to the cutoff so that's not great but it is a more significant result here the significance point 0 0 3 so that's a little better looking at the total variance explained we're now down to four factors that explains 60% of the variance and of course that's indicated by the scree plot you can see there's only four components above an eigen value of one and now when we look at the rotated component matrix we can see an item 1 we have three values that load or in component one we have three values that load item two item forward item five as we move down kind of a stair-step effect we can see that item 10 and eight load fairly well together on component two and then we can see for component three that item one does not load very well and item six and I am three load pretty well and then you have that that item I component for that has item seven it's just sitting by itself at point eight six eight so there's nothing else that really loads with that too strongly so a possibility here would be to now remove item one and see if that improves the properties of our instrument so we go back so now we'll just take out item one run the same analysis again no problems seen here on the correlation matrix barely acceptable result on kmo we have four factors still but they explain 64% of the variance instead of 60% and the prior analysis and of course the scree plot still the four components and looking at the rotated component matrix we can see that component one loads well together with this or two items load weld together in component one then we have to that load well on component two to that load well on component three and then item seven item four on component for there okay I think this is an acceptable result I really look for a factor loading here of 0.45 or greater and this is 0.47 six so it's close but it's there so you could say that item seven I'm for load together fairly well not ideally as kind of these other loadings for three two and one are both or all of them are point above 0.7 so not great but certainly acceptable and that really is the process of running factor analysis you're you're looking at the constructs from the results and you're making adjustments on items that you're going to include usually you would start with more than ten items of course most assessments in counseling or have more than ten items and then as you see the results by writing the factor analysis you remove those items with lo factor loadings until you get an instrument and theory that has a rotated component matrix that looks more like what I have here I hope you found this video on conducting a factor analysis with a ver max rotation and SPSS to be helpful 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: 141,011

Rating: 4.890954 out of 5

Keywords: SPSS, factor analysis, exploratory factor analysis, principal components analysis, PCA, varimax, varimax rotation, determinant, eigenvalue, KMO, Bartlett, sphericity, Statistics (Field Of Study), Factor, Principal Component Analysis, counseling, Grande

Id: d588GFOEnP0

Length: 16min 12sec (972 seconds)

Published: Fri May 15 2015