{"id":356,"date":"2019-01-01T04:54:26","date_gmt":"2019-01-01T04:54:26","guid":{"rendered":"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=356"},"modified":"2019-01-01T05:24:14","modified_gmt":"2019-01-01T05:24:14","slug":"factor-analysis-using-r","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/chapter\/factor-analysis-using-r\/","title":{"rendered":"Factor Analysis using R"},"content":{"raw":"&nbsp;\r\n\r\n<strong>1 Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Factor analysis is a technique that is used to reduce a large number of variables into fewer numbers of factors. This technique extracts maximum common vari-ance from all variables and puts them into a common score. As an index of all variables, we can use this score for further analysis.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Factor analysis can be considered an extension of principal component analysis. Both can be viewed as attempts to approximate the covariance matrix. However the approximation based on the factor analysis model is more elaborate.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-359\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03.jpg\" alt=\"\" width=\"1085\" height=\"1381\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-360\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04.jpg\" alt=\"\" width=\"969\" height=\"297\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-361\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05.jpg\" alt=\"\" width=\"1037\" height=\"933\" \/>\r\n<p style=\"text-align: justify\">We are rst going to see how many factors are required to best explain the data. We perform eigen analysis of the sample correlation matrix from the rst prin-ciples. We nd the cumulative proportion of variability explained by factors<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-362\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06.jpg\" alt=\"\" width=\"1049\" height=\"1009\" \/>\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-363\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07.jpg\" alt=\"\" width=\"1233\" height=\"1145\" \/>\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-364\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08.jpg\" alt=\"\" width=\"911\" height=\"901\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-365\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09.jpg\" alt=\"\" width=\"1265\" height=\"627\" \/>\r\n\r\n&nbsp;\r\n\r\n<strong>Interpretation:<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">The score corresponding to \"Endurance\" (Factor 1) is more for the 4th individual as compared to the 6th individual. Looking at the data cor-responding to the two individuals we see that for the 4th individual time taken to complete a longer distance race i.e 5k, 10k or Marathon is less as compared to the 6th individual.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">Likewise the score corresponding to \"Strenth\" (Factor 2) is more for the 6th individual as compared to the 4th individual. Looking at the data corresponding to the two individuals we see that for the 6th individual time taken to complete a shorter distance race i.e 100m, 200m, etc is less as compared to the 4th individual.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-366\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10.jpg\" alt=\"\" width=\"1089\" height=\"1585\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-367\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11.jpg\" alt=\"\" width=\"1349\" height=\"1277\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-368\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12.jpg\" alt=\"\" width=\"1093\" height=\"1325\" \/>\r\n\r\n<strong>SUMMARY<\/strong>\r\n<ul>\r\n \t<li style=\"text-align: justify\">In R we can perform Factor Analysis using inbuilt R functions<\/li>\r\n \t<li style=\"text-align: justify\">If the data is available in raw<span style=\"text-align: initial;font-size: 1em\"> form we can go for either estimation using Principal Component method of Maximum Likelihood method and also estimate the factor scores<\/span><\/li>\r\n \t<li style=\"text-align: justify\">If the data is not available in raw form, but we have the correlation or dis-persion<span style=\"text-align: initial;font-size: 1em\"> matrix, we can only go for estimation using Principal Component method and estimate the factor scores from <\/span>rst<span style=\"text-align: initial;font-size: 1em\"> principles<\/span><\/li>\r\n \t<li style=\"text-align: justify\">If the variables are highly correlated amongst themselves we achieve Di-mension<span style=\"text-align: initial;font-size: 1em\"> Reduction using Factor Analysis, <\/span>however<span style=\"text-align: initial;font-size: 1em\"> such dimension <\/span>reduc-tion<span style=\"text-align: initial;font-size: 1em\"> is not <\/span>signi<span style=\"text-align: initial;font-size: 1em\"> cant if the correlations are low<\/span><\/li>\r\n<\/ul>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 References<\/strong>\r\n<ul>\r\n \t<li>R.A.Johnson &amp; D.W. Wichern, Applied Multivariate Statistical Analysis, Pearson<\/li>\r\n \t<li>T.W. Anderson, An Introduction to Multivariate Analysis, John Wiley<\/li>\r\n \t<li>G.A.F. Seber, Multivariate Observations, John Wiley<\/li>\r\n \t<li>N.C. Giri, Multivariate Statistical Inference, Academic Press<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;","rendered":"<p>&nbsp;<\/p>\n<p><strong>1 Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Factor analysis is a technique that is used to reduce a large number of variables into fewer numbers of factors. This technique extracts maximum common vari-ance from all variables and puts them into a common score. As an index of all variables, we can use this score for further analysis.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Factor analysis can be considered an extension of principal component analysis. Both can be viewed as attempts to approximate the covariance matrix. However the approximation based on the factor analysis model is more elaborate.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-359\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03.jpg\" alt=\"\" width=\"1085\" height=\"1381\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03.jpg 1085w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03-236x300.jpg 236w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03-768x978.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03-805x1024.jpg 805w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03-65x83.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03-225x286.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-03-350x445.jpg 350w\" sizes=\"auto, (max-width: 1085px) 100vw, 1085px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-360\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04.jpg\" alt=\"\" width=\"969\" height=\"297\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04.jpg 969w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04-300x92.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04-768x235.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04-65x20.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04-225x69.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-04-350x107.jpg 350w\" sizes=\"auto, (max-width: 969px) 100vw, 969px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-361\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05.jpg\" alt=\"\" width=\"1037\" height=\"933\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05.jpg 1037w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05-300x270.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05-768x691.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05-1024x921.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05-65x58.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05-225x202.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-05-350x315.jpg 350w\" sizes=\"auto, (max-width: 1037px) 100vw, 1037px\" \/><\/p>\n<p style=\"text-align: justify\">We are rst going to see how many factors are required to best explain the data. We perform eigen analysis of the sample correlation matrix from the rst prin-ciples. We nd the cumulative proportion of variability explained by factors<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-362\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06.jpg\" alt=\"\" width=\"1049\" height=\"1009\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06.jpg 1049w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06-300x289.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06-768x739.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06-1024x985.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06-65x63.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06-225x216.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-06-350x337.jpg 350w\" sizes=\"auto, (max-width: 1049px) 100vw, 1049px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-363\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07.jpg\" alt=\"\" width=\"1233\" height=\"1145\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07.jpg 1233w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07-300x279.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07-768x713.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07-1024x951.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07-65x60.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07-225x209.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-07-350x325.jpg 350w\" sizes=\"auto, (max-width: 1233px) 100vw, 1233px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-364\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08.jpg\" alt=\"\" width=\"911\" height=\"901\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08.jpg 911w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08-300x297.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08-768x760.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08-65x64.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08-225x223.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-08-350x346.jpg 350w\" sizes=\"auto, (max-width: 911px) 100vw, 911px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-365\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09.jpg\" alt=\"\" width=\"1265\" height=\"627\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09.jpg 1265w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09-300x149.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09-768x381.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09-1024x508.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09-65x32.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09-225x112.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-09-350x173.jpg 350w\" sizes=\"auto, (max-width: 1265px) 100vw, 1265px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Interpretation:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The score corresponding to &#8220;Endurance&#8221; (Factor 1) is more for the 4th individual as compared to the 6th individual. Looking at the data cor-responding to the two individuals we see that for the 4th individual time taken to complete a longer distance race i.e 5k, 10k or Marathon is less as compared to the 6th individual.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Likewise the score corresponding to &#8220;Strenth&#8221; (Factor 2) is more for the 6th individual as compared to the 4th individual. Looking at the data corresponding to the two individuals we see that for the 6th individual time taken to complete a shorter distance race i.e 100m, 200m, etc is less as compared to the 4th individual.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-366\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10.jpg\" alt=\"\" width=\"1089\" height=\"1585\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10.jpg 1089w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10-206x300.jpg 206w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10-768x1118.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10-704x1024.jpg 704w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10-65x95.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10-225x327.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-10-350x509.jpg 350w\" sizes=\"auto, (max-width: 1089px) 100vw, 1089px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-367\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11.jpg\" alt=\"\" width=\"1349\" height=\"1277\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11.jpg 1349w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11-300x284.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11-768x727.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11-1024x969.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11-65x62.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11-225x213.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-11-350x331.jpg 350w\" sizes=\"auto, (max-width: 1349px) 100vw, 1349px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-368\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12.jpg\" alt=\"\" width=\"1093\" height=\"1325\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12.jpg 1093w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12-247x300.jpg 247w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12-768x931.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12-845x1024.jpg 845w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12-65x79.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12-225x273.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2019\/01\/1525695488FactorAnalysisUsingR-12-350x424.jpg 350w\" sizes=\"auto, (max-width: 1093px) 100vw, 1093px\" \/><\/p>\n<p><strong>SUMMARY<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify\">In R we can perform Factor Analysis using inbuilt R functions<\/li>\n<li style=\"text-align: justify\">If the data is available in raw<span style=\"text-align: initial;font-size: 1em\"> form we can go for either estimation using Principal Component method of Maximum Likelihood method and also estimate the factor scores<\/span><\/li>\n<li style=\"text-align: justify\">If the data is not available in raw form, but we have the correlation or dis-persion<span style=\"text-align: initial;font-size: 1em\"> matrix, we can only go for estimation using Principal Component method and estimate the factor scores from <\/span>rst<span style=\"text-align: initial;font-size: 1em\"> principles<\/span><\/li>\n<li style=\"text-align: justify\">If the variables are highly correlated amongst themselves we achieve Di-mension<span style=\"text-align: initial;font-size: 1em\"> Reduction using Factor Analysis, <\/span>however<span style=\"text-align: initial;font-size: 1em\"> such dimension <\/span>reduc-tion<span style=\"text-align: initial;font-size: 1em\"> is not <\/span>signi<span style=\"text-align: initial;font-size: 1em\"> cant if the correlations are low<\/span><\/li>\n<\/ul>\n<div>\n<p><strong>\u00a0 \u00a0 References<\/strong><\/p>\n<ul>\n<li>R.A.Johnson &amp; D.W. Wichern, Applied Multivariate Statistical Analysis, Pearson<\/li>\n<li>T.W. Anderson, An Introduction to Multivariate Analysis, John Wiley<\/li>\n<li>G.A.F. Seber, Multivariate Observations, John Wiley<\/li>\n<li>N.C. Giri, Multivariate Statistical Inference, Academic Press<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"author":3,"menu_order":23,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-sumitra-purkayastha"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-356","chapter","type-chapter","status-publish","hentry","contributor-prof-sumitra-purkayastha"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/356","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":3,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/356\/revisions"}],"predecessor-version":[{"id":369,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/356\/revisions\/369"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/356\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/media?parent=356"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapter-type?post=356"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/contributor?post=356"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/license?post=356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}