Factor Loading in Factor Analysis

factor loading it's a major component of factor analysis and principal component analysis they both use this so how it works is you have a bunch of survey questions and you're gonna create a bunch of new component variables also called factors I call them new factors latent variables what they're gonna be is whatever this new variable is is gonna have several of these questions that all are strongly correlated which means they're being answered similarly so let's just let's just do one so let's take question one we run a correlation between that and the new component which is made up of several other other questions and we get the correlation so the first correlation to component one is pretty high 0.58 we do the same thing for component 2 and for component 3 right we want correlations between the individual item and each of the new components to check their correlations so the second one is 0.1 one nothing to write home about and the third one is point negative o8 so there's no question about it that question number one belongs under component number one because it loading factor is greater than point four so the loading factor it again is basically the correlation right so it's obvious with question number one they're not always this obvious not every item will load neatly like question number one did so the software is going to determine under which of the new components each one of these survey questions should go with because it's got the the highest correlation or the highest loading factor so let's just pretend the computer did them all you do the magic of video and so component one has these questions - as these questions three has these questions now you're gonna run into something that that is problematic with factor loading with factor analysis altogether every once in a while you're gonna get a question that doesn't load up so nicely so let's just pretend question seven we ran three correlations between the three new components and we got the correlation of 0.47 for the first one point 4 2 for the second one point 1 3 for the third one so it's obviously the third one is not going to be yet but look how close 1 & 2 are right so this one is a little bit bigger but we're only talking about 5/100 of a bigger correlation and number 2 so it's not a big difference this is what we call overlap now we try to get rid of overlap by using a rotation the orthogonal rotation that's the berry max on spss normally does a really good job of what I call raking out any overlap between which quest which new component these items should go under but it doesn't get rid of all of it okay so but again a rotation will remove the overlap but sometimes it won't okay sometimes there's too much overlap between the two and that can become problematic it's up to the researcher to decide which one of these items should be under which component right like we could have put number 7 under number 2 and the results would probably be minimal but we never know for sure okay let's try something else you also might run into something that like like this here's question number 10 and we do the three correlations between the three new components and we get different numbers so the first correlation is negative point zero nine that's tiny that's not gonna go and then 0.16 that's not greater than point four so that wouldn't go there this one is not greater than point for either okay so this number ten really doesn't correlate very well with any of these so you might want to think of not using that question under number ten all right do not use number ten because it doesn't really correlate with any of the new factors so you would just remove this question out just pull it out what I'm gonna do I'm gonna run one real quick for you in SPSS so I can show you that what's going on here okay so please hold I made this survey a long time ago trying to gauge the fear of statistics that many students have and I made it so we would reverse code everything so what that means is strong one is strongly agree two is agree but all the way down to five is strongly disagree now I would reverse CODIS so a five would mean I strongly agree so the larger the number we add all these up to create a new variable the larger the number the more fearful of stats somebody is but again after we recode diesease is a different it's a different video okay but now we're gonna go to analyze dimension reduction get in there you factor and what do you know they're already in there so there's the 23 questions okay so under descriptives you want all of these things univariate initial everything on the left-hand side click continue extraction this is the default principal component analysis I don't use scree plots and put one in there just for you guys based on eigen values greater than one so we need any new component that has an eigen value greater than one will be considered a new factor okay if you know beforehand that you only want to come out with three factors you can click that button and type in three right based on research or something but if not don't worry about it click it out click continue' rotation we tend to use berry max first that's an orthogonal rotation in other words it tries to pull out as much overlap between these items as possible if you think your new factors are gonna be somehow correlated to each other you should probably use the oblique rotation which is the direct Oberman but we tend to use bare Max and it automatically does the rotated solutions for you scores we could keep these as new variables if you want in other words the new factors would be saved as new factors we're not gonna do that in this video and then our options this is the important stuff right here right we're gonna put them in order by size and we don't want an item if it doesn't load up with at least point four that's what this is right here right this is where you decide what you want your load of loading factor minimum to be and we tend to use point four sometimes we use point three but depending on which book you're reading click continue click OK and check out the results here so here's the means and standard deviations of each item don't really care about that here's the correlation table really don't care about that you get correlations all over to play significant ones again this is just the factor loading video so let's just go right to commonalities this is the extraction number also known as the loading factor these are the loading factors so again anything that's less than point four is gonna be problematic for you so you know point four that means that this first question statistics makes me cry does load up significantly under one of the new factors let's see how many new factors we got here oh we didn't do that yet and then I'm here from right so you look at the eigenvalue so out of our twenty three questions whatever it was we got four new components right so there's gonna be four new components wake up here so that means that question one does load up under one of the four pretty good pretty good pretty good pretty good this one right here three point four three I don't understand statistics doesn't load up so well right only point three four remember that I don't like statistics and there's another one computers are useful only for video games and computers are out to get me so anything that loads up under less than point four could be problematic it looks like it we have one two three four here but not always because these were pretty close to four so I'm predicting that they will not be problematic here's the four new components let's go down and see her scree plot anything over one here you can be considered a new factor and we don't really need scree plus because we know there's four and this is the component matrix but it has not been rotated so don't use this one go down to the rotated so under the first new factor right all these questions kind of clearly go under the first factor okay there's our computers are out to get me computers hate me so even though it loaded up kind of poorly from the extraction it did quite well under the component and these are the questions that go under number two so you notice this one it has overlap right it's under 0.47 three under component 1 but on point five to 302 so the larger the number that should be the winner component so it does go under two and these other ones this goes under these three go under component three and these go under component four so I don't see any problems there whatsoever even though some of the loadings were not quite over point four so that was that in a nutshell I hope it helped them gz out Matt guys zero

Channel: Math Guy Zero

Views: 3,516

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Keywords: Math Guy Zero, Math, Stats, Statistics

Id: KlmCmT7k-cw

Length: 10min 13sec (613 seconds)

Published: Tue Jun 30 2020