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NOTE: On April 2, 2018 I updated this video with a new video that goes, step-by-step, through PCA and how it is performed. Check it out! https://youtu.be/FgakZw6K1QQ RNA-seq results often contain a PCA or MDS plot. This StatQuest explains how these graphs are generated, how to interpret them, and how to determine if the plot is informative or not. I've got example code (in R) for how to do PCA and extract the most important information from it on the StatQuest website: https://statquest.org/2015/08/13/pca-clearly-explained/ For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider a StatQuest t-shirt or sweatshirt... https://teespring.com/stores/statquest ...or buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest
Factor Analysis and PCA Factor Analysis Factor Analysis @0:10 Job Satisfaction @0:21 Satisfied with Pay @0:37 Principle Component Analysis @1:18 Factor Analysis & Principle Component Analysis @2:40 #Exclude #Reduction #Variance #Factor #Component #Variance #Influence #Communalities #Manishika #Examrace Reduce large number of variables into fewer number of factors Co-variation is due to latent variable that exert casual influence on observed variables Communalities – each variable’s variance that can be explained by factors Principal Component Analysis Variable reduction process – smaller number of components that account for most variance in set of observed variables Explain maximum variance with fewest number of principal components PCA Factor Analysis Observed variance is analyzed Shared variance is analyzed 1.00’s are put in diagonal – all variance in variables Communalities in diagonal – only variance shared with other variables are included – exclude error variance and variance unique to each variable Analyze variance Analyze covariance NET Psychology postal course - https://www.examrace.com/CBSE-UGC-NET/CBSE-UGC-NET-FlexiPrep-Program/Postal-Courses/Examrace-CBSE-UGC-NET-Psychology-Series.htm NET Psychology MCQs - https://www.doorsteptutor.com/Exams/UGC/Psychology/ IAS Psychology - https://www.examrace.com/IAS/IAS-FlexiPrep-Program/Postal-Courses/Examrace-IAS-Psychology-Series.htm IAS Psychology test series - https://www.doorsteptutor.com/Exams/IAS/Mains/Optional/Psychology/
Views: 7409 Examrace
-Introduction to factor analysis -Factor analysis vs Principal Component Analysis (PCA) side by side Read in more details - https://www.udemy.com/principal-component-analysis-pca-and-factor-analysis/?couponCode=GP_TR_1
Views: 11903 Gopal Malakar
July 31, 2015 - Genetic Counseling Training Program. More: http://www.genome.gov/27558706
The main ideas behind PCA are actually super simple and that means it's easy to interpret a PCA plot: Samples that are correlated will cluster together apart from samples that are not correlated with them. In this video, I walk through the ideas so that you will have an intuitive sense of how PCA plots are draw. If you'd like more details, check out my full length PCA video here: https://youtu.be/_UVHneBUBW0 For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider a StatQuest t-shirt or sweatshirt... https://teespring.com/stores/statquest ...or buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest
Data Science for Biologists Dimensionality Reduction: Principal Components Analysis Part 1 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton
Views: 78841 Data4Bio
In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 1 of 6). Youtube SPSS factor analysis Principal Component Analysis YouTube Channel: https://www.youtube.com/user/statisticsinstructor Subscribe today! Lifetime access to SPSS videos: http://tinyurl.com/m2532td Video Transcript: In this video we'll take a look at how to run a factor analysis or more specifically we'll be running a principal components analysis in SPSS. And as we begin here it's important to note, because it can get confusing in the field, that factor analysis is an umbrella term where the whole subject area is known as factor analysis but within that subject there's two types of main analyses that are run. The first type is called principal components analysis and that's what we'll be running in SPSS today. And the other type is known as common factor analysis and you'll see that come up sometimes. But in my experience principal components analysis is the most commonly used procedure and it's also the default procedure in SPSS. And if you look on the screen here you can see there's five variables: SWLS 1, 2 3, 4 and 5. And what these variables are they come from the items of the Satisfaction with Life Scale published by Diener et al. And what people do is they take these five items they respond to the five items where SLWS1 is "In most ways my life is close to my ideal;" and then we have "The conditions of my life are excellent;" "I am satisfied with my life;" "So far I've gotten the important things I want in life;" and then SWLS5 is "If I could live my life over I would change almost nothing." So what happens is the people respond to these five questions or items and for each question they have the following responses, which I've already input here into SPSS value labels: strongly disagree all the way through strongly agree, which gives us a 1 through 7 point scale for each question. So what we want to do here in our principal components analysis is we want to go ahead and analyze these five variables or items and see if we can reduce these five variables or items into one or a few components or factors which explain the relationship among the variables. So let's go ahead and start by running a correlation matrix and what we'll do is we're going to Analyze, Correlate, Bivariate, and then we'll move these five variables over. Go ahead and click OK and then here notice we get the correlation matrix of SWLS1 through SWLS5. So these are all the intercorrelations that we have here. And if we look at this off-diagonal where these ones here are the diagonal. And they're just a one because of variable is correlated with itself so that's always 1.0. And then the off-diagonal here represents the correlations of the items with one another. So for example this .531 here; notice it says in SPSS that the correlation is significant at the .01 level, two tailed. So this here is the correlation between SWLS2 and SLWS1. So all of these in this triangle here indicate the correlation between the different variables or items on the Satisfaction with Life Scale. And what we want to see here in factor analysis which we're about to run is that these variables are correlated with one another and at a minimum significantly so. Because what factor analysis or principal components analysis does is that it analyzes the correlations or relationships between our variables and basically we try to determine a smaller number of variables that can explain these correlations. So notice here we're starting with five variables, SWLS1 through five. Well hopefully in this analysis when we run our factor analysis we'll come out with one component that does a good job of explaining all these correlations here. And one of the key points of factor analysis is it's a data reduction technique. What that means is we enter a certain number of variables, like five in this example, or even 20 or 50 or what have you, and we hope to reduce those variables down to just a few; between one and let's say 5 or 6 is most of the solutions that I see. Now in this case since we have five variables we really want to reduce this down to 1 or 2 at most but 1 would be good in this case. So that's really a key point of factor analysis: we take a number of variables and we try to explain the correlations between those variables through a smaller number of factors or components and by doing that what we do is we get more parsimonious solution, a more succinct solution that explains these variables or relationships. And there's a lot of applications of factor analysis but one of the primary ones is when you're analyzing scales or items on a scale and you want to see how that scale turns out, so how many dimensions or factors doesn't it have to it.
Principal Component Analysis, is one of the most useful data analysis and machine learning methods out there. It can be used to identify patterns in highly complex datasets and it can tell you what variables in your data are the most important. Lastly, it can tell you how accurate your new understanding of the data actually is. In this video, I go one step at a time through PCA, and the method used to solve it, Singular Value Decomposition. I take it nice and slowly so that the simplicity of the method is revealed and clearly explained. There is a minor error at 1:47: Points 5 and 6 are not in the right location If you are interested in doing PCA in R see: https://youtu.be/0Jp4gsfOLMs For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider a StatQuest t-shirt or sweatshirt... https://teespring.com/stores/statquest ...or buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest
This video demonstrates conducting a factor analysis (principal components analysis) with varimax rotation in SPSS.
Views: 89454 Dr. Todd Grande
A Webcast to accompany my 'Discovering Statistics Using ....' textbooks. This webcast looks at how to do Factor Analysis on SPSS and interpret the output.
Views: 134706 Andy Field
Currell: Scientific Data Analysis. Minitab analysis for Figs 9.6 and 9.7 http://ukcatalogue.oup.com/product/9780198712541.do © Oxford University Press
I demonstrate how to perform a principal components analysis based on some real data that correspond to the percentage discount/premium associated with nine listed investment companies. Based on the results of the PCA, the listed investment companies could be segmented into two largely orthogonal components.
Views: 206476 how2stats
Watch on Udacity: https://www.udacity.com/course/viewer#!/c-ud262/l-649069103/m-661438544 Check out the full Advanced Operating Systems course for free at: https://www.udacity.com/course/ud262 Georgia Tech online Master's program: https://www.udacity.com/georgia-tech
Views: 293722 Udacity
In this video, we cover how to interpret a scree plot in factor analysis. Click here for our entire factor analysis series: https://www.youtube.com/watch?v=ajvpIACCyd4&list=PLRV_2nAtkiVMwQm1mko_Pb9I3mF_4KKwS
Video covers - Overview of Principal Componets Analysis (PCA) and why use PCA as part of your machine learning toolset - Using princomp function in R to do PCA - Visually understanding PCA
Views: 83245 Melvin L
Determining the efficiency of a number of variables in their ability to measure a single construct. Link to Monte Carlo calculator: http://www.allenandunwin.com/spss4/further_resources.html Download the file titled MonteCarloPA.zip.
This video demonstrates how conduct an exploratory factor analysis (EFA) in SPSS. The Principal Axis Factoring (PAF) method is used and compared to Principal Components Analysis (PCA).
Views: 16475 Dr. Todd Grande
This video provides an introduction to factor analysis, and explains why this technique is often used in the social sciences. Check out https://ben-lambert.com/econometrics-course-problem-sets-and-data/ for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: https://ben-lambert.com/bayesian/ Accompanying this series, there will be a book: https://www.amazon.co.uk/gp/product/1473916364/ref=pe_3140701_247401851_em_1p_0_ti
Views: 195563 Ben Lambert
This video demonstrates how interpret the SPSS output for a factor analysis. Results including communalities, KMO and Bartlett’s Test, total variance explained, and the rotated component matrix are interpreted.
Views: 145930 Dr. Todd Grande
We've talked about the theory behind PCA in https://youtu.be/FgakZw6K1QQ Now we talk about how to do it in practice using R. If you want to copy and paste the code I use in this video, it's right here: https://statquest.org/2017/11/27/statquest-pca-in-r-clearly-explained/ For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider a StatQuest t-shirt or sweatshirt... https://teespring.com/stores/statquest ...or buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/
This video provides an overview of Principal components analysis in SPSS as a data reduction technique (keep in mind the assumption is you are working with measured variables that are reasonably treated as continuous). I review basic options in SPSS, as well as discuss strategies for identifying the number of components to retain (including parallel analysis) and naming those factors. I discuss Varimax rotation and Promax rotation, as well as the generation of component scores. Finally, I illustrate how you can use component scores in subsequent analyses such as regression. This is a fairly long video, but it was aimed at being comprehensive! You can perform the same steps I illustrate by downloading the data here ( https://drive.google.com/open?id=1Ds7LXr-_NUP3FYCxcd0kxv9WHowUwGqc ) and following along. You can go to the site referenced to carry out the parallel analysis here: https://analytics.gonzaga.edu/parallelengine/ The IBM website referencing the KMO measure of sampling adequacy is located here: http://www-01.ibm.com/support/docview.wss?uid=swg21479963 For more instructional videos and other materials on various statistics topics, be sure to my webpages at the links below: Introductory statistics: https://sites.google.com/view/statisticsfortherealworldagent/home Multivariate statistics: https://sites.google.com/view/statistics-for-the-real-world/home
Views: 9399 Mike Crowson
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Views: 35658 5 Minutes Engineering
In this video you will learn about Principal Component Analysis (PCA) and the main differences with Exploratory Factor Analysis (EFA). Also how to conduct the PCA analysis on SPSS and interpret its results.
Views: 64707 educresem
In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 3 of 6). YouTube Channel: https://www.youtube.com/user/statisticsinstructor Subscribe today! Video Transcript: we'll also pull up our Scree plot here. These two tables here, the Total Variance Explained and Scree Plot, both deal with what's known as our factor extraction methods. If you recall when we went through SPSS, the options, we left the eigenvalue greater than one rule option selected as the default, but we also selected that a Scree plot be output in our analysis. And these are two of the most commonly used procedures for deciding how many components or factors to retain; how many do you want to keep in our solution. Here for our Total Variance Explained table, notice first of all that we have 5 components in our rows here. And you may be wondering, well wait a second, I thought factor analysis, the whole purpose of it, was to reduce our number of variables into a smaller number of components? And if you are thinking that, you're correct, that is our purpose here. But, as just a matter of definition, it's always the case that the number of variables we input in our analysis, will always be equal to the number of components shown here. So we have five variables input in our analysis, therefore we have 5 rows or 5 components shown here. Now here in our Initial Eigenvalues table, notice that we have these various eigenvalues. So the first one is 3.136 and everything after that is less than 1. Now if you recall our first rule was eigenvalue greater than one rule. So that was, keep the number of factors or components that have eigenvalues greater than one. All other components with eigenvalues less than one, such as these here, we do not keep. If you look at the Extraction Sums of Squared Loadings section of this table, notice that there's only one value here now. And what this means is this is how many components SPSS retained or kept, based on the rule. So since only one component had an eigenvalue greater than one, we only have one component in our solution here. So the results of this rule tells us, or indicates, that we want to have one component. So in other words, we reduce those 5 variables down to one component. Or that one component, from this perspective, does a pretty good job at explaining the relationships between SWLS1 through SWLS5. One way to assess how good of a job this analysis did at explaining the relationships between those variables, is to look at the percent of variance accounted for by the component. And in this example, our one component solution accounted for 62.72% of the variance, or about 63% of variance, which is pretty good in practice. I typically see solutions between 40% and 60% of the variance, in the 40s through 60s, in that range. I don't typically see many solutions with variance higher than 70, and a solution below 40 is not very strong. But that's typically the range that I'll see them in, so I would say that 63% is pretty good in practice. Now an interesting thing here, recall that we had 5 components. If you add up these eigenvalues they will equal to 5, within rounding error. So the sum of the eigenvalues is always equal to the number of components, or put another way, the number of original variables in your analysis. So if I had 10 variables in my analysis here, then these values would sum up to 10. And in fact would be 10 rows in this table. Now since I have 5 variables, I'm going to have 5 components output in my initial solution, and the eigenvalues will sum to 5. And the reason why that's good to know is that if you divide the eigenvalue for our retained component the 3.136/5 you will get exactly .6272 or 62.72% when converted to a percentage. So the percent of variance accounted for is literally the magnitude of the eigenvalue divided by the sum of the eigenvalues, or 5 in this case. OK, so in summary, our eigenvalue greater than one rule indicated that one component should be retained. Next let's look at the Scree plot. So here our Scree plot, notice first of all that on the X-axis, the component number is plotted, so this is the first component, second component, third, and so on. And on the Y-axis we have our eigenvalue plotted. And in fact if you think about it, this graph is really just plotting, notice this first value, 3.136, that is right here. Component 2 is somewhere between .6 and .7, and if you look here, here we go component 2, .625. Notice component 3 drops off just a little, it is .534 Component 4 is .463, and then component 5 is .231. So this Scree plot is literally just these eigenvalues plotted from left to right. Now the rule of thumb for interpreting the Scree plot is as follows:
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Representing multivariate random signals using principal components. Principal component analysis identifies the basis vectors that describe the largest fraction of the variance in the observed data. It is used to find a low-dimensional representation for high-dimensional signals. PCA can be used to improve the SNR by a factor of N/p where the signal has p components, the noise is white, and the data dimension is N.
Views: 8199 Barry Van Veen
In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 2 of 6). YouTube Channel: https://www.youtube.com/user/statisticsinstructor Subscribe today! Video Transcript: to Dimension Reduction. And first of all, notice that name there, dimension reduction. The key here, reduction, we're trying to reduce a certain number of variables or items to a smaller number of factors or components. And we can refer to these as dimensions, so if we have one factor that's a one dimension(al) solution, two factors is a two dimension(al) solution, and so on. Let's go ahead and select Factor. And then here we want to move all our variables over to the right. Go ahead and select Descriptives, and then we'll select Univariate descriptives, to get some univariate descriptive statistics on each of our variables. And I also want to select KMO and Bartlett's test of sphericity. Then we'll click Continue. And then next we go to Extraction and notice here, by default, the method is principal components. And that's what I had mentioned that we're going to run here today. So that's good, we want to leave that selected. But if you are looking for an alternative procedure, you can find a number of them here. Now We're just going to do principal components, which I said earlier, is the most commonly used method of analysis. OK we'll go ahead and leave these defaults, we'll have the Unrotated factor solution displayed, and then I also want to display a Scree plot, which I'll tell you about more in a few minutes. And then let's leave this Extraction default option selected. So notice that the extraction is, based on eigenvalue, where eigenvalues greater than 1 will be retained or extracted. And I will go into that in detail in just a few moments. So go ahead and click Continue. OK Rotations, let's go ahead and look at that. Now I'll go and select Varimax, and we'll see what happens when we run the analysis. But notice here we have five different options. The first thing to note is that there's two key types of rotation, there's Orthogonal rotation, and there's Oblique rotation. Now orthogonal rotation means that your factors or components, if there is more than one, if there's two or more factors or components, they will be uncorrelated. In fact that rotational solution forces them to be uncorrelated. Now oblique, on the other hand, they're rotated in such a way where they're allowed to be correlated. So you'll get solutions where the factors typically will be correlated to some degree. But the oblique rotation allows for the correlation. Now of these rotation procedures in SPSS, Varimax, Quartimax and Equamax are all different types of orthogonal, or uncorrelated rotations, whereas Direct Oblimin and Promax are oblique, or correlated rotations. We'll go and select Varimax in this case. OK go ahead and click Continue. And then that looks good, so go ahead and click OK. And then here we have our analysis, and our first table we'll look at here is the KMO and Bartlett's test. This is sometimes reported, so I want to be sure that you understand what it is here. Bartlett's test the sphericity, that's what we're going to be focusing on. And Bartlett's test of sphericity, notice first of all, that it is significant, it's less than .05. And it approximates a chi-square distribution, so we can consider it chi-square distributed. And what this is testing is, it's actually testing whether this correlation matrix, are these variables, so item 1 with 2, item 1 with 3, item 2 with 3, and so on, this entire triangle are these variables, are they correlated significantly different than zero. But unlike the correlation matrix, it doesn't test each individual correlation separately, but what it does is, in one overall test, it assesses whether these 10 correlations, taken as a group, do they significantly differ from zero. And more precisely, for those who are familiar with matrix algebra, it's testing whether this correlation matrix is significantly different than an identity matrix. An identity matrix just has ones along the main diagonal and zeros in all other places. So in other words, it's a matrix where variables are not correlated whatsoever with each other, but as always, a variable correlates 1.0 with itself. So it has 1s on the main diagonal, 0 everywhere else. And the fact that this is significant, and it's extremely significant, the p-value is very small, it gives us confidence that our variables are significantly correlated. So once again that's testing whether the variables, as a set, does this matrix, does this group of variables, differ significantly from all zeros here, and it definitely does. So that's what that test measures. OK next we have our commonalities, and I'm going to skip over that for a minute, we'll get back to that soon though. Let's go and look at the total variance explained.
Video tutorial on running principal components analysis (PCA) in R with RStudio. Please view in HD (cog in bottom right corner). Download the R script here: https://drive.google.com/open?id=1tbiHCdPnptP4SzQVzH1-t5Q1EJ4Y2uBR
Views: 24395 Hefin Rhys
This video walks you through some basic methods of Principal Component Analysis like generating screeplots, factor loadings and predicting factor scores
Views: 24455 MKT Res
Video illustrates use of Principal components analysis in SPSS for the purposes of data reduction. Illustrates how to reduce a set of measured variables to a smaller set of components for inclusion as predictors in a regression analysis. Illustrates use of component scores. Parallel analysis demonstration provided using Parallel analysis engine found at http://ires.ku.edu/~smishra/parallelengine.htm
Views: 11484 Mike Crowson
Step by step detail with example of Principal Component Analysis PCA Read in more details - https://www.udemy.com/principal-component-analysis-pca-and-factor-analysis/?couponCode=GP_TR_1 Also if you just want to understand it high level without mathematics, you can refer to this link https://www.youtube.com/watch?v=8BKFd9izEXM
Views: 117085 Gopal Malakar
Introduction to factor analysis/ principal components analysis including interpretation. Do I need to run a factor analysis (FA)? Questionnaires with inter-related questions, summarising content of lots of questions (items) by a few factors, creating scores for attributes, validity of a scale, checking a scale is unidimensional for Cronbach Alpha Types of FA: exploratory and confirmatory Steps in perfoming EFA Example: EFA on personaility data NOTE: somewhere in the video I say you can compute mean and standard deviations of the estimated factor scores. Well, you can, but it;s not meaningful. To see how people scored on a factor, a histogram or QQ plot would do.
Views: 68639 Phil Chan
I demonstrate how to perform a principal components analysis based on some real data that correspond to the percentage discount/premium associated with nine listed investment companies. Based on the results of the PCA, the listed investment companies could be segmented into two largely orthogonal components.
Views: 111522 how2stats
Subject:Statistics Paper: Multivariate analysis
Views: 282 Vidya-mitra
Views: 934 IvyProSchool
In this video, we look at how to run an exploratory factor analysis (principal components analysis) in SPSS (Part 4 of 6). YouTube Channel: https://www.youtube.com/user/statisticsinstructor Subscribe today! Video Transcript: what we want to do is retain the number of components that are above what's known as the scree, or where this plot tends to not drop much, when it tends to, I wouldn't say flatline, but taper off very gradually. Notice how these 4points here, these 4 eigenvalues, the rate of change, or the slope here, is quite minimal as we move across. But this value, there's a big drop from component 1 to component 2, and then from component 2 all the way through 5, there's not much of a change anymore. So according to the scree plot, we interpret the number of components above where they tend to not change much anymore. And where this name comes from, the scree plot, scree is a geological term which indicates the rubble or the stones that fall from a cliff. So if you think of a cliff, you're driving along the road, you're going to see a lot of stones, smaller sized rocks and some bigger rocks, but they're all collected along the side of the mountain, right? Well this is the scree or the rubble that is collected off the cliff. So that's where this name comes from. So we want to retain the number of components above the scree. So the scree plot would indicate to us here that we want to retain one component. Suppose there was a component right here as well. Well notice that it still drops quite a bit from here to here, and then it flat lines. So if we had a component here as well, then we would retain two components in that case. As you add components the likelihood of these two rules of thumb agreeing completely, decreases. It certainly can happen, they can agree, without question, but the likelihood tends to decrease. One of the interesting things about these two rules are that, the eigenvalue greater than one rule has been around for a very long time, as has the scree plot. The eigenvalue greater than one rule was published by Kaiser in 1960, so that's quite a long time, and it's still one of the primary methods for extraction, for determining the number of components, used today. And the scree plot, the key publication for that was in 1966 by Raymond Cattell. So this came out in 66, the publication anyway, and the publication for this came out in 1960 by Kaiser, so that's quite a long time ago, and they're still the two primary methods that are used for factor extraction. Now that being said, for those who are interested in a more advanced look at factor analysis, there are better methods that can be used, such as parallel analysis. But, unfortunately, they're not output in SPSS. You can go ahead and run a parallel analysis if you search on the web, and you can use syntax for SPSS to run it, or you can use, some websites have it all ready, where you just input the number of variables you have, your sample size, and so on, and you can get out the solution for the parallel analysis. But that's really beyond the scope of this video. If I get a chance, I'll try to make a video on how to run and interpret a parallel analysis as well. But for now, these are the two most commonly used methods of extraction. OK, so to review, in our example here, we have one component. And next we'll go ahead and look at our Component Matrix and we'll also look at our Rotated Component Matrix here. And let's start with this one. Notice it says Rotated Component Matrix only one component was extracted the solution cannot be rotated. And that's a very important point to make, and that is, when you have a one component solution in principal components analysis, then there is no rotation. Rotation only comes into play when there are two or more components. So with one component there is no rotation, and that's why we got this output, and the reason why we got this output, if you recall, when we did our factor analysis in SPSS, under rotation, we asked for Varimax. So basically SPSS is telling us, we can't do Varimax rotation because there's only one component, and rotation doesn't come into play in that case. So as one measure of the effectiveness of our solution, we noted the total variance explained by our one component. I had said that 63% of the variance was pretty good in practice. That's one way to look at it. That's the overall variance that the component accounts for. Now here on the Component Matrix
Full lecture: http://bit.ly/PCA-alg We can find the direction of the greatest variance in our data from the covariance matrix. It is the vector that does not rotate when we multiply it by the covariance matrix. Such vectors are called eigenvectors, and have corresponding eigenvalues. Eigenvectors that have the largest eigenvalues will be the principal components (new dimensions of our data).
Views: 81156 Victor Lavrenko
In this video you will learn Principal Component Analysis using SaS. You will learn how to perform PCA using Proc Factor and Proc Princomp For Training & Study packs on Analytics/Data Science/Big Data, Contact us at [email protected] Find all free videos & study packs available with us here: http://analyticuniversity.com/ SUBSCRIBE TO THIS CHANNEL for free tutorials on Analytics/Data Science/Big Data/SAS/R/Hadoop SUBSCRIBE TO THE CHANNEL. FOR ONLINE TRAINING or RECORDED VIDEOS, CONTACT [email protected] For details visit: https://docs.google.com/document/d/17N9_Gd-VuDqz9TwV8aSoyoZoFgg17gQyzxNht-P_MZY/edit
Views: 11847 Analytics University