Principal components analysis and factor analysis are two techniques that have different histories, but overlap in the computational procedures used. Strictly speaking, principal components is a descriptive procedure used to project a multivariate data set into a space with fewer dimensions. The first principal component is the direction of maximum covariance (or correlation) through the data cloud. The second is the direction of the next highest covariance (correlation) that is also uncorrelated with the previous component, etc. The principal component loadings indicate generally which variables are important in defining each component.
Factor analysis attempts to discover latent variables under the assumption that the measured variables are "caused" by unobservable factors and the correlations between the observed variables provide evidence of these latent variables. Factors are often initially extracted using principal components analysis and then rotated so that they are more interpretable. The rotation tries to create factors with either very low or very high loadings for each variable. Psychologists generally come from a factor analysis background and tend to prefer rotated factors. Researchers using principal components to simplify their data to look for clusters or other patterns prefer to keep the original components since they reflect the covariance structure of the data in a way that is lost by rotation. Your latest post suggests that you are planning to use the components in a regression analysis - hence as latent variables. Rotation may make it easier to interpret those components. Multidimensional scaling will give you something analogous to unrotated principal components but you do not get loadings so you have no easy way to relate the MDS dimensions back to the original variables (although you could run correlations between the original variables and the mds dimensions to get similar information). ------------------------------------- David L Carlson Associate Professor of Anthropology Texas A&M University College Station, TX 77840-4352 From: Elizabeth Beck [mailto:elizabethbe...@gmail.com] Sent: Monday, June 17, 2013 1:43 PM To: Bert Gunter Cc: David Carlson; r-help@r-project.org Subject: Re: [R] NMDS with missing data? Hi Bert & David - I'm putting aside the issues with the missing data for the moment - the NAs are due to not enough sample volume for testing and there are only about 6 of them for 1 variable. I have multiple data sets to look and not all with missing values. I do intend to find some local consulting options once I have a bit more of a grasp on my options. If I were to stick with the principal() function using my standardized variables...rotate=none would make sense initially, although several papers I have read with very similar data sets have used a Varimax factor rotation (orthogonal transformation). My reasoning behind the PCA is to reduce the number of variables (as many are likely correlated) and then use those new factors to run a perMANOVA. All of my categorical factors are explanatory variables (sex, exposure, treatment) so will be used in the final model. Is PCA still the preferred ordination method for this type of data? Are there advantages to NMDS instead? I appreciate the input... Elizabeth On Mon, Jun 17, 2013 at 12:28 PM, Bert Gunter <gunter.ber...@gene.com> wrote: David et. al.: I hate to be a pest but ... On Mon, Jun 17, 2013 at 11:02 AM, David Carlson <dcarl...@tamu.edu> wrote: > First, Bert is correct. I should have said to use prcomp(dat, center=TRUE, scale=TRUE). That will run the svd on the standardized variables which is equivalent to using princomp(dat, cor=TRUE). ***You will have to remove the cases with missing variables or impute the missing variables using one of many options in R. *** Depending on the number of missings and nature of the missingness, this can be a crucial issue. Omitting all data with missing entries makes very strong assumptions about the nature of the missingness and can lead to highly biased results. Which is problematic for exploration, even. The same is true with imputation -- you need to do it properly. Again, depending on the number of cases at issue. So it may be wise for Elizabeth to consult a local statistical expert and not rely on superficial background from a text and remote advice. There may be dragons ... Cheers, Bert > > The principal() function in package psych should be fine and will probably give nearly identical results. It does have the ability to generate a pairwise-deletion correlation matrix so you could include your cases with missing values. I would set rotate="none" least initially. Hopefully your text will explain why this is a good idea. > > I assume you are looking for interesting patterns in the data rather than trying to test a specific hypothesis. Given that, you should try both (or all three with principal()) and see if there are any interesting differences between them. > > Earlier I asked if all your variables are numeric (or dichotomies). If any are categorical (factors), these suggestions may have to be revised. > > ------------------------------------- > David L Carlson > Associate Professor of Anthropology > Texas A&M University > College Station, TX 77840-4352 > > > -----Original Message----- > From: Bert Gunter [mailto:gunter.ber...@gene.com] > Sent: Monday, June 17, 2013 12:35 PM > To: Elizabeth Beck > Cc: David Carlson; r-help@r-project.org > Subject: Re: [R] NMDS with missing data? > > Just wanted to note that one does **not** use > "prcomp() on the correlation matrix of the variables." > > As ?prcomp says, it uses the svd of the data matrix, which is > generally preferable. > > Cheers, > Bert > > On Mon, Jun 17, 2013 at 10:02 AM, Elizabeth Beck > <elizabethbe...@gmail.com> wrote: >> Hello David, >> >> Yes my variables are all numeric....I have a few questions regarding your 2 >> options. >> >> Would these still be the best options if missing data was not an issue? I >> was told that I should be performing NMDS as it has few assumptions on the >> data distribution but neither of your options use this. >> >> If NMDS is not preferred and I were to perform a PCA, can you tell me why >> you chose prcomp()? My statistical text (Discovering Statistics Using R) >> explains PCA quite well using principal() in the psych package so I am just >> wondering the advantages of one over the other... I am overwhelmed by the >> number of ordination methods! >> >> Thank you, >> Elizabeth >> >> On Mon, May 13, 2013 at 9:44 AM, David Carlson <dcarl...@tamu.edu> wrote: >> >>> First. Do not use html messages. They are converted to plain text and your >>> table ends up a mess. See below. It appears the variables are all numeric? >>> If so, there are two standard approaches to handling multiple scales and >>> magnitudes with cluster analysis: >>> >>> 1. Use z-scores. The scale() function will convert each variable into a >>> standard score with a mean of 0 and a standard deviation of 1. Then use >>> Euclidean distance in the dist() function which will adjust for your >>> missing >>> values. >>> >>> 2. Use prcomp() on the correlation matrix of the variables to extract a set >>> of principal components and use the principal component scores in the >>> cluster analysis. This may allow you to reduce the number of variables in >>> the data set if the 29 variables are correlated with one another. >>> >>> ------------------------------------- >>> David L Carlson >>> Associate Professor of Anthropology >>> Texas A&M University >>> College Station, TX 77840-4352 >>> >>> From: Elizabeth Beck [mailto:elizabethbe...@gmail.com] >>> Sent: Friday, May 10, 2013 1:20 PM >>> To: dcarl...@tamu.edu >>> Cc: r-help@r-project.org >>> Subject: Re: [R] NMDS with missing data? >>> >>> Hi David, >>> >>> You are right in that Bray-Curtis is not suitable for my dataset, and that >>> my variables are very different. Given your suggestions, I am struggling >>> with how to transform or standardize my data given that they vary so much. >>> Additionally, looking at the dist() package I am not sure which distance >>> measure would be most appropriate. Euclidean seems to most widely used but >>> I'm not sure if it is appropriate for myself (there much more help for >>> ecology data than toxicology). Given a sample of my data below ( total of >>> 287 obs. of 29 variables) can you suggest a starting point? >>> >>> SODIUM >>> K >>> CL >>> HCO3 >>> ANION >>> CA >>> P >>> GLUCOSE >>> CHOLEST >>> GGT >>> GLDH >>> CK >>> AST >>> PROTEIN >>> ALBUMIN >>> GLOBULIN >>> A_G >>> UA >>> BA >>> CORTICO >>> T3 >>> T4 >>> THYROID >>> 145 >>> 3.3 >>> 102 >>> 24 >>> 22 >>> 2.9 >>> 2.45 >>> 9.8 >>> 5.7 >>> 3 >>> 3 >>> 678 >>> 5 >>> 34 >>> 15 >>> 19 >>> 0.79 >>> 180 >>> 6 >>> 70.97 >>> 1.31 >>> 12.77 >>> 0.102376 >>> 146 >>> 3.2 >>> 102 >>> 21 >>> 26 >>> 2.89 >>> 2.68 >>> 11.1 >>> 6.78 >>> 3 >>> 4 >>> 1290 >>> 9 >>> 36 >>> 18 >>> 18 >>> 1 >>> 170 >>> 13 >>> 79.1 >>> 3.51 >>> 18.78 >>> 0.186751 >>> 147 >>> 2.5 >>> 103 >>> 22 >>> 25 >>> 2.96 >>> 2.59 >>> 10 >>> 5.78 >>> 3 >>> 6 >>> 1582 >>> 11 >>> 35 >>> 17 >>> 18 >>> 0.94 >>> 272 >>> 10 >>> 65.84 >>> 1.84 >>> 15.5 >>> 0.118602 >>> 148 >>> 2.5 >>> 101 >>> 21 >>> 29 >>> 2.91 >>> 2.91 >>> 10.6 >>> 5.83 >>> 3 >>> 3 >>> 1479 >>> 8 >>> 35 >>> 17 >>> 18 >>> 0.94 >>> 317 >>> 8 >>> 74.9 >>> 2.59 >>> 20.68 >>> 0.125389 >>> >>> Thank you! >>> Elizabeth >>> >>> On Thu, May 9, 2013 at 7:50 AM, David Carlson <dcarl...@tamu.edu> wrote: >>> Since you pass your entire data.frame to metaMDS(), your first error >>> probably comes from the fact that you have included ID as one of the >>> variables. You should look at the results of >>> >>> str(dat) >>> >>> You can drop cases with missing values using >>> >>> > dat2 <- na.omit(dat) >>> > metaMDS(dat2[,-1]) >>> >>> would run the analysis on all but the first column (ID) with all the cases >>> containing complete data. But that assumes that sex and exposure are not >>> factors. >>> >>> Or you could use one of the distance functions in dist() which adjust for >>> missing values. However dist() does not have an option to use Bray-Curtis >>> (the default in metaMDS()). Bray-Curtis is designed for comparing species >>> counts or proportions so it is not clear that it is an appropriate >>> dissimilarity measure for your data. Further, your data seem contain a >>> mixture of measurement scales and/or magnitudes so some variable >>> standardization or transformations are probably necessary before you can >>> get >>> any useful results from MDS. >>> >>> ------------------------------------- >>> David L Carlson >>> Associate Professor of Anthropology >>> Texas A&M University >>> College Station, TX 77840-4352 >>> >>> -----Original Message----- >>> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] >>> On >>> Behalf Of Elizabeth Beck >>> Sent: Wednesday, May 8, 2013 3:39 PM >>> To: r-help@r-project.org >>> Subject: [R] NMDS with missing data? >>> >>> Hi, >>> I'm trying to run NMDS (non-metric multidimensional scaling) with R vegan >>> (metaMDS) but I have a few NAs in my data set. I've tried to run it 2 ways. >>> >>> The first way with my entire data set which includes variables such as ID, >>> sex, exposure, treatment, sodium, potassium, chloride.... >>> >>> mydata.mds<-metaMDS(dat) >>> >>> I get the following error: >>> >>> in if (any(autotransform, noshare > 0, wascores) && any(comm < 0)) { : >>> missing value where TRUE/FALSE needed >>> In addition: Warning messages: >>> 1: In Ops.factor(left, right) : < not meaningful for factors >>> 2: In Ops.factor(left, right) : < not meaningful for factors >>> 3: In Ops.factor(left, right) : < not meaningful for factors >>> 4: In Ops.factor(left, right) : < not meaningful for factors >>> 5: In Ops.factor(left, right) : < not meaningful for factors >>> >>> The second way with only those last biochemical variables (29 in total). >>> >>> mydata.mds<-metaMDS(measurements) >>> >>> I get this error: >>> >>> Error in if (any(autotransform, noshare > 0, wascores) && any(comm < 0)) { >>> : >>> missing value where TRUE/FALSE needed >>> >>> My go to "na.rm=TRUE" does nothing. Any ideas on how to account for NAs and >>> if so which of the above options I should be using? >>> Thanks! >>> Elizabeth >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide >>> http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >>> >>> >>> >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > > > -- > > Bert Gunter > Genentech Nonclinical Biostatistics > > Internal Contact Info: > Phone: 467-7374 > Website: > http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/p db-biostatistics/pdb-ncb-home.htm > -- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/p db-biostatistics/pdb-ncb-home.htm ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
