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This video demonstrates conducting a factor analysis (principal components analysis) with varimax rotation in SPSS.
Views: 88121 Dr. Todd Grande
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
In this video, we are going to see exactly how we can perform dimensionality reduction with a famous Feature Extraction technique - Principal Component Analysis PCA. We’ll get into the math that powers it REFERENCES  Computing Eigen vectors and Eigen values: https://www.scss.tcd.ie/~dahyotr/CS1BA1/SolutionEigen.pdf  Diagonalizing a Matrix: http://mathworld.wolfram.com/MatrixDiagonalization.html  Step by step diagonalization: https://yutsumura.com/how-to-diagonalize-a-matrix-step-by-step-explanation/#Step_2_Find_the_eigenvalues IMAGE REFERENCES  Gene Expression: https://geneed.nlm.nih.gov/topic_subtopic.php?tid=15&sid=22  Graph_plot: https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues/140579#140579  Eigenvecotrs: https://commons.wikimedia.org/wiki/File:Eigenvectors.gif
Views: 6787 CodeEmporium
This video covers the types of rotation in a factor analysis, including orthogonal (uncorrelated) and oblique (correlated) rotation. orthogonal rotation in factor analysis oblique rotation in factor analysis Factor Analysis, Principal Components Analysis, Rotation, Methods of rotation, oblique rotation, orthogonal rotation, Varimax, Oblimin, Quartimax, Equamax
This video demonstrates how to select a rotation in a factor analysis (principal components analysis) using SPSS. Rotations assist in the interpretation of factor analysis results. Several rotations including varimax, quartimax, equamax direct oblimin, and promax are reviewed.
Views: 17884 Dr. Todd Grande
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: 80066 Victor Lavrenko
For SCMA643 @ VCU.
Views: 3346 Chris Merritt
Watch on Udacity: https://www.udacity.com/course/viewer#!/c-ud262/l-649069103/m-661438545 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: 100780 Udacity
Currell: Scientific Data Analysis. Minitab analysis for Figs 9.6 and 9.7 http://ukcatalogue.oup.com/product/9780198712541.do © Oxford University Press
Explore the rotation of the PCA results in the energy space in order to make them more interpretable. Find more information at http://temdm.com
Views: 63 TEMDM
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
This video lecture describes the relation between correlation analysis and PCA.
Views: 12312 QualityAndTechnology
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: 204518 how2stats
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: 6514 Examrace
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: 191752 Ben Lambert
Principal component analysis (PC), design matrix rotation, constraints that cause multicollinearity, and principal component regression. Course Website: http://www.lithoguru.com/scientist/statistics/course.html
Views: 2316 Chris Mack
Principal Component Analysis and Factor Analysis https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis
Views: 90300 econometricsacademy
Principal Component Analysis and Factor Analysis in R https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis
Views: 106458 econometricsacademy
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: 8199 Mike Crowson
This video walks you through some basic methods of Principal Component Analysis like generating screeplots, factor loadings and predicting factor scores
Views: 23868 MKT Res
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: 142346 Dr. Todd Grande
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.
Principal Component Analysis and Factor Analysis in Stata https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis
Views: 110942 econometricsacademy
Navigation on video fragments: http://www.rotmistrov.com/faen (after entering, use the navigation area on the page's right side) Considering the topic of trust types, one may find in ESS database interpersonal trust indicators and indicators of the trust in political institutions (i.e., political trust). If one factorize these indicators, he may gain one two-components joint factor model or two one-component pure factor models. One should take into account that the components are genetically correlated. Therefore, one should choose between an oblique joint model or two correlated pure models. If an oblique joint model is chosen, one should select the respective rotation settings. In contrast, if the set of pure models is chosen, one may not keep in mind selecting rotation settings.
Principal Component Analysis and Factor Analysis Example https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis
Views: 67814 econometricsacademy
UGC-NET Psychology
This video shows you how to conduct and write up a principal component analysis in SPSS. Both varimax and oblimin rotation are covered
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.
I perform a PCA on a set of six MSCI indices. First, I go download the data and import it into R with readxl. Then I look at the data and the returns with some very basic techniques like plotting the performance with ggplot and tidyquant. Later I perform a PCA and also apply a varimax transformation on the loadings (the eigenvectors). Lastly, I look at how an equal-weighted portfolio performed versus a portfolio with components selected based on the PCA/varimax results. It's not fully as desired but (we want higher Sharpe ratio of course), but interesting nevertheless.
Views: 529 Martin Geissmann
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.
See https://www.survo.fi/demos/index.html#ex38
Views: 2353 Seppo Mustonen
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: 133309 Andy Field
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
Applied Multivariate Statistical Modeling by Dr J Maiti,Department of Management, IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
Views: 8371 nptelhrd
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: 64263 educresem
-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: 11412 Gopal Malakar
# PCA with function prcomp pca1 = prcomp(geno, scale. = TRUE) #Performs a principal components analysis on the given data matrix and returns the results as an object of class prcomp summary(pca1) # loadings pca1_loading = pca1\$x #the value of the rotated data (the centred data multiplied by the rotation matrix) # add cluster info to pca pca1_loading = cbind(GDmerged[,1:5], pca1_loading) names(pca1_loading) = "Name" dat4 = pca1_loading #percent variance explained to use in x and y axis in graph PCA = as.matrix(pca1) # make figure colored by pca tiff("Subpopulation_pca.tiff", width = 4, height = 3, units = 'in', res = 300) ggplot(dat4, aes(x = PC1, y = PC2, color = GenetBackground)) + geom_point(alpha=0.5) + labs(x = "PC1 (44.8%)", y = "PC2 (31.49%)")+ theme_classic()+ scale_color_brewer(palette="Set1")+ theme(axis.text=element_text(size=12), axis.title=element_text(size=14,face="bold")) dev.off()
Views: 548 Kevin Falk
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: 16092 Dr. Todd Grande
Views: 3144 Jinsuh Lee
Principal Component Analysis and Factor Analysis in SAS https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis
Views: 24631 econometricsacademy
Configure a simple principal component analysis and interpret the outputs. Discover our products: https://www.xlstat.com/en/solutions Go further: https://help.xlstat.com/customer/en/portal/articles/2062222 30-day free trial: https://www.xlstat.com/en/download -- Stat Café - Question of the Day is a playlist aiming at explaining simple or complex statistical features with applications in Excel and XLSTAT based on real life examples. Do not hesitate to share your questions in the comments. We will be happy to answer you. -- Produced by: Addinsoft Directed by: Nicolas Lorenzi Script by: Jean Paul Maalouf
Views: 17379 XLSTAT
Dr. Manishika Jain in this lecture explains factor analysis. Introduction to Factor Analysis: Factor Loading, Factor Scoring & Factor Rotation. 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/ Steps in Research Proposal @0:24 Research Topic @0:43 Review of Literature @0:56 Rationale and Need for the Study @1:18 Definition of Terms @1:24 Assumptions @3:03 Method, Sample and Tools @4:06 Probability Sampling @4:23 Non - Probability Sampling @4:34 Significance of Study @5:13 Technique for Data Analysis @5:18 Bibliography @5:42 Budget @6:28 Chapterisation @6:39 #Expenditure #Tabulate #Significance #Assumption #Literature #Rationale #Constitutive #Phenomena #Elucidate #Literature #Manishika #Examrace Factor Analysis and PCA 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 Types of Factoring • PCA – maximum variance for 1st factor; removes that and uses maximum for 2nd factor and so on… • Common Factor Analysis – Same as factor analysis (only common variance – used in CFA) • Image Factoring – correlation matrix; uses OLS regression matrix • Maximum Likelihood Method – on correlation matrix • Alpha Factoring • Weight Square Estimate communalities - each variable’s variance that can be explained by factor. See factors are retained Factor rotation - Procedure in which the eigenvectors (factors) are rotated in an attempt to achieve simple structure. Factor loading - Relation of each variable to the underlying factor. Output of a simple factor analysis looking at indicators of wealth, with just six variables and two resulting factors 6 variables: Income, education, occupation, house value, public parks and crimes 2 factors: individual socioeconomic status and neighborhood socioeconomic status Factor Score – if value of variables are given then factor values can be predicted Interpretation
Views: 15687 Examrace
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
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: 110386 how2stats
Video illustrates use of Principal components analysis in SPSS. Begins with illustration of reverse-coding items from a survey. Then illustrates assessing appropriateness of PCA/factor analysis using KMO and Bartlett's test of sphericity. Reviews use of Kaiser criterion (eigenvalue cutoff of 1), scree plot, and parallel analysis to determine number of components to maintain. Reviews use of Varimax rotation in interpreting component loadings. Parallel analysis demonstration provided using Parallel analysis engine found at http://ires.ku.edu/~smishra/parallelengine.htm
Views: 3707 Mike Crowson
Learn how to reduce many variables to a few significant variable combinations, or principal components. See how to create the components on covariances, correlations, or unscaled; examine the contribution of each variable to the related principal component; and save the principal component values to the data table for future analysis.
Views: 11786 JMPSoftwareFromSAS
This video covers factor (component) loadings in factor analysis. Click here for free access to all of our videos: https://www.youtube.com/user/statisticsinstructor (Remember to click on "Subscribe") factor loadings component loadings factor analysis
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: 11272 Mike Crowson
How to characterize the principal components? How to describe the dimensions? How to use qualitative variables to describe the results of PCA? Is the percentage of variance (percentage of inertia) associated to each dimension important or not?
Views: 3719 François Husson