1 / 10

Analysis Using R

Analysis Using R. 1.Finds the classical scaling solution. 2. Computes the Trace criterion & Magnitude criterion to determine the # of dimensions. (1*). R>voles_mds<- cmdscale(watervoles, k=13, eig=TRUE). R>voles_mds$eig

dorinda-urbina
Download Presentation

Analysis Using R

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Analysis Using R 1.Finds the classical scaling solution. 2. Computes the Trace criterion & Magnitude criterion to determine the # of dimensions. (1*) R>voles_mds<- cmdscale(watervoles, k=13, eig=TRUE) R>voles_mds$eig [1] 7.359910e-01 2.626003e-01 1.492622e-01 6.990457e-02 2.956972e-02 1.931184e-02 8.326673e-17 -1.139451e-02 -1.279569e-02 -2.849924e-02 [11] -4.251502e-02 -5.255450e-02 -7.406143e-02

  2. We have 13 eigenvalues, some positive & some negative. R>sum(abs(voles_mds$eig[1:2]))/ sum (abs(voles_mds$eig)) [1] 0.6708889 This code satisfies Magnitude Criterion. (2*) R>sum((voles_mds$eig[1:2])^2/ sum((voles_mds$eig)^2) [1] 0.9391378 Which is the criteria suggested by Mardia et al.; the above code is exactly: k n ∑│λ│ / ∑ │λ│ i=1 i=1 0.6708889 & .9391378 are large enough to suggest that the original distances Between water vole populations can be represented adequately in two dimensions. (3*)

  3. R>x<- voles_mds$points[, 1] 1: Coordinate 1 R>y<-voles_mds$points[, 2] 2: Coordinate 2 R>plot(x,y,xlab= "Coordinate 1", ylab= "Coordinate 2", xlim= range(x) * 1.2, type= "n") R>text(x,y, labels= colnames(watervoles)) 6 British populations are close to populations living in the Alps, Yugoslavia, Germany, Norway, & Pyrenees I. (Arvicola terrestris) These British populations are distant from the populations in Pyrenees II, North Spain and South Spain. (Arvicola sapidus) (4*)

  4. Minimum Spanning Tree (MDS solution) highlight possible distortions. (5,6*) Links of a minimum spanning tree of the proximity matrix may be plotted onto the two-dimensional scaling representation to identify distortions (if any) produced by scaling solutions. These distortions look like nearby points on the plot that are not linked by an edge of a tree. (7*) R>library("ape") R>st<- mst(watervoles) R>plot(x,y,xlab= "Coordinate 1", ylab= "Coordinate 2", xlim= range (x) * 1.2, type= "n") R>for (i in 1:nrow(watervoles)) { + w1<- which(st[i, ] == 1) + segments(x[i], y[i], x[w1], y[w1]) } R>text(x, y, labels= colnames(watervoles))

  5. The apparent closeness of the populations, Germany & Norway, by the points suggested here in this MDS solution, does not reflect accurately their calculated dissimilarity. (8*)

  6. Non-Metric Scaling Example: Analyzing Voting Behavior among Republicans. R Function isoMDS from package “MASS” R>library("MASS") R>data("voting", package= "HSAUR") R>voting_mds<- isoMDS(voting)

  7. Two-Dimensional Solution: R>x<- voting_mds$points[, 1] R>y<- voting_mds$points[, 2] R>plot(x,y, xlab="Coordinate 1", ylab= "Coordinate 2", + xlim= range(voting_mds$points[, 1]) *1.2, + type= "n" ) R>text(x,y, labels= colnames(voting)) R>voting_sh<- Shepard(voting[ lower.tri(voting)], + voting_mds$points Figure suggests that there is more variation in voting behavior among Republicans. (*9)

  8. R>library("MASS") R>voting_sh<- Shepard(voting[lower.tri(voting)], + voting_mds$points) R>plot(voting_sh, pc= ".", xlab= "Dissimilarity", + ylab= "Distance", xlim= range(voting_sh$x), + ylim= range(voting_sh$x)) R>lines(voting_sh$x, voting_sh$yf, type= "S") Quality of a multidimensional scaling can be assessed informally by plotting the original dissimilarities & the distances obtained from a multidimensional scaling in a scatterplot. Ideally, all the lines should fall on the bisecting line.

More Related