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Stata added or improved a number of multivariate procedures is Stata 9. Stata 10 continues to imrpove upon multivariate techniques by adding full k-group discriminant function analysis, adding multiple correspondence analysis (mca), and by improving the multideminsional scaling (mds) program.
1: Discriminant analysis
Stata has added the following discriminant analysis procedures:We will demonstrate examples of these commands using Fisher's Iris example.
use http://www.ats.ucla.edu/stat/stata/seminars/stata10/iris, clear
candisc sl sw pl pw, group(type)
Canonical linear discriminant analysis
| | Like-
| Canon. Eigen- Variance | lihood
Fcn | Corr. value Prop. Cumul. | Ratio F df1 df2 Prob>F
----+---------------------------------+------------------------------------
1 | 0.9848 32.1919 0.9912 0.9912 | 0.0234 199.15 8 288 0.0000 e
2 | 0.4712 .285391 0.0088 1.0000 | 0.7780 13.794 3 145 0.0000 e
---------------------------------------------------------------------------
Ho: this and smaller canon. corr. are zero; e = exact F
Standardized canonical discriminant function coefficients
| function1 function2
-------------+----------------------
sl | -.4269549 -.0124077
sw | -.5212416 -.7352612
pl | .9472573 .4010379
pw | .5751607 -.5810398
Canonical structure
| function1 function2
-------------+----------------------
sl | .2225959 -.3108118
sw | -.1190115 -.8636809
pl | .7060654 -.1677014
pw | .6331779 -.7372421
Group means on canonical variables
type | function1 function2
-------------+----------------------
setosa | -7.6076 -.215133
versicolor | 1.825049 .7278996
virginica | 5.78255 -.5127666
Resubstitution classification summary
+---------+
| Key |
|---------|
| Number |
| Percent |
+---------+
| Classified
True type | setosa versicolor virginica | Total
-------------+------------------------------------+-----------
setosa | 50 0 0 | 50
| 100.00 0.00 0.00 | 100.00
| |
versicolor | 0 48 2 | 50
| 0.00 96.00 4.00 | 100.00
| |
virginica | 0 1 49 | 50
| 0.00 2.00 98.00 | 100.00
-------------+------------------------------------+-----------
Total | 50 49 51 | 150
| 33.33 32.67 34.00 | 100.00
| |
Priors | 0.3333 0.3333 0.3333 |
estat manova
Number of obs = 150
W = Wilks' lambda L = Lawley-Hotelling trace
P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F
-----------+--------------------------------------------------
type | W 0.0234 2 8.0 288.0 199.15 0.0000 e
| P 1.1919 8.0 290.0 53.47 0.0000 a
| L 32.4773 8.0 286.0 580.53 0.0000 a
| R 32.1919 4.0 145.0 1166.96 0.0000 u
|--------------------------------------------------
Residual | 147
-----------+--------------------------------------------------
Total | 149
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F
/* group summarize */
estat grsummarize
Estimation sample candisc
Summarized by type
| type
Mean | setosa versicolor virginica | Total
-------------+------------------------------------+-----------
sl | 5.006 5.936 6.588 | 5.843333
sw | 3.428 2.77 2.974 | 3.057333
pl | 1.462 4.26 5.552 | 3.758
pw | .246 1.326 2.026 | 1.199333
-------------+------------------------------------+-----------
N | 50 50 50 | 150
/* Mahalanobis squared distances between the group means */
estat grdistances
Mahalanobis squared distances between groups
| type
type | setosa versicolor virginica
-------------+-----------------------------------
setosa | 0
versicolor | 89.864186 0
virginica | 179.38471 17.201066 0
label define tl 1 "S" 2 "C" 3 "V", modify
scoreplot, msymbol(i)
discrim qda sl sw pl pw, group(type)
Quadratic discriminant analysis
Resubstitution classification summary
+---------+
| Key |
|---------|
| Number |
| Percent |
+---------+
| Classified
True type | setosa versicolor virginica | Total
-------------+------------------------------------+-----------
setosa | 50 0 0 | 50
| 100.00 0.00 0.00 | 100.00
| |
versicolor | 0 48 2 | 50
| 0.00 96.00 4.00 | 100.00
| |
virginica | 0 1 49 | 50
| 0.00 2.00 98.00 | 100.00
-------------+------------------------------------+-----------
Total | 50 49 51 | 150
| 33.33 32.67 34.00 | 100.00
| |
Priors | 0.3333 0.3333 0.3333 |
discrim logistic sl sw pl pw, group(type)
Iteration 0: log likelihood = -164.79184
Iteration 1: log likelihood = -67.780459
(omitted)
Iteration 22: log likelihood = -5.9492736
Iteration 23: log likelihood = -5.9492736
Logistic discriminant analysis
Resubstitution classification summary
+---------+
| Key |
|---------|
| Number |
| Percent |
+---------+
| Classified
True type | setosa versicolor virginica | Total
-------------+------------------------------------+-----------
setosa | 50 0 0 | 50
| 100.00 0.00 0.00 | 100.00
| |
versicolor | 0 49 1 | 50
| 0.00 98.00 2.00 | 100.00
| |
virginica | 0 1 49 | 50
| 0.00 2.00 98.00 | 100.00
-------------+------------------------------------+-----------
Total | 50 50 50 | 150
| 33.33 33.33 33.33 | 100.00
| |
Priors | 0.3333 0.3333 0.3333 |
discrim knn sl sw pl pw, group(type) k(3)
Kth-nearest-neighbor discriminant analysis
Resubstitution classification summary
+---------+
| Key |
|---------|
| Number |
| Percent |
+---------+
| Classified
True type | setosa versicolor virginica | Total
-------------+------------------------------------+-----------
setosa | 50 0 0 | 50
| 100.00 0.00 0.00 | 100.00
| |
versicolor | 0 47 3 | 50
| 0.00 94.00 6.00 | 100.00
| |
virginica | 0 3 47 | 50
| 0.00 6.00 94.00 | 100.00
-------------+------------------------------------+-----------
Total | 50 50 50 | 150
| 33.33 33.33 33.33 | 100.00
| |
Priors | 0.3333 0.3333 0.3333 |
2: Correspondence analysis
Correspondence analysis has been improved by adding multiple correspondence analysis (mca) to the existing simple correspondence analysis (ca).
use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear
/* ca from What's New in Stata 9 */
ca prog ses
Correspondence analysis Number of obs = 200
Pearson chi2(4) = 16.60
Prob > chi2 = 0.0023
Total inertia = 0.0830
3 active rows Number of dim. = 2
3 active columns Expl. inertia (%) = 100.00
| singular principal cumul
Dimension | value inertia chi2 percent percent
------------+------------------------------------------------------------
dim 1 | .2604912 .0678557 13.57 81.73 81.73
dim 2 | .1231525 .0151665 3.03 18.27 100.00
------------+------------------------------------------------------------
total | .0830222 16.60 100
Statistics for row and column categories in symmetric normalization
| overall | dimension_1 | dimension_2
Categories | mass quality %inert | coord sqcorr contrib | coord sqcorr contrib
-------------+---------------------------+---------------------------+---------------------------
prog | | |
general | 0.225 1.000 0.249 | 0.442 0.555 0.169 | 0.576 0.445 0.606
academic | 0.525 1.000 0.384 | -0.482 0.997 0.469 | -0.039 0.003 0.006
vocation | 0.250 1.000 0.367 | 0.615 0.807 0.363 | -0.437 0.193 0.387
-------------+---------------------------+---------------------------+---------------------------
ses | | |
low | 0.235 1.000 0.247 | 0.432 0.558 0.168 | 0.559 0.442 0.597
middle | 0.475 1.000 0.180 | 0.270 0.603 0.133 | -0.319 0.397 0.392
high | 0.290 1.000 0.573 | -0.792 0.996 0.699 | 0.069 0.004 0.011
-------------------------------------------------------------------------------------------------
/* mca for Stata 10 */
mca prog ses female
Multiple/Joint correspondence analysis Number of obs = 200
Total inertia = .0353896
Method: Burt/adjusted inertias Number of axes = 2
| principal cumul
Dimension | inertia percent percent
------------+----------------------------------
dim 1 | .0182501 51.57 51.57
dim 2 | .0075739 21.40 72.97
dim 3 | .000025 0.07 73.04
------------+----------------------------------
Total | .0353896 100.00
Statistics for column categories in standard normalization
| overall | dimension_1 | dimension_2
Categories | mass quality %inert | coord sqcorr contrib | coord sqcorr contrib
-------------+---------------------------+---------------------------+---------------------------
prog | | |
general | 0.075 0.699 0.098 | 1.152 0.524 0.099 | 1.030 0.174 0.080
academic | 0.175 0.736 0.151 | -1.096 0.719 0.210 | 0.260 0.017 0.012
vocation | 0.083 0.748 0.144 | 1.265 0.478 0.133 | -1.474 0.270 0.181
-------------+---------------------------+---------------------------+---------------------------
ses | | |
low | 0.078 0.727 0.179 | 1.392 0.438 0.152 | 1.754 0.288 0.241
middle | 0.158 0.760 0.085 | 0.434 0.181 0.030 | -1.203 0.579 0.229
high | 0.097 0.743 0.235 | -1.839 0.716 0.327 | 0.550 0.027 0.029
-------------+---------------------------+---------------------------+---------------------------
female | | |
male | 0.152 0.678 0.059 | -0.418 0.230 0.027 | -0.905 0.448 0.124
female | 0.182 0.678 0.050 | 0.349 0.230 0.022 | 0.756 0.448 0.104
-------------------------------------------------------------------------------------------------
3: Multidimensional scaling
Improved multideminsional scaling (mds) addingg for modern metric and nonmetric MDS in addition to classical multidimensional scaling.
use http://www.stata-press.com/data/r10/cerealnut, clear
mds calories-K, id(brand) method(classical)
Classical metric multidimensional scaling
dissimilarity: L2, computed on 8 variables
Number of obs = 25
Eigenvalues > 0 = 8 Mardia fit measure 1 = 0.9603
Retained dimensions = 2 Mardia fit measure 2 = 0.9970
--------------------------------------------------------------------------
| abs(eigenvalue) (eigenvalue)^2
Dimension | Eigenvalue Percent Cumul. Percent Cumul.
-------------+------------------------------------------------------------
1 | 158437.92 56.95 56.95 67.78 67.78
2 | 108728.77 39.08 96.03 31.92 99.70
-------------+------------------------------------------------------------
3 | 10562.645 3.80 99.83 0.30 100.00
4 | 382.67849 0.14 99.97 0.00 100.00
5 | 69.761715 0.03 99.99 0.00 100.00
6 | 12.520822 0.00 100.00 0.00 100.00
7 | 5.7559984 0.00 100.00 0.00 100.00
8 | 2.2243244 0.00 100.00 0.00 100.00
--------------------------------------------------------------------------
mds calories-K, id(brand) method(modern) loss(strain) transform(ident)
Iteration 1: strain = 594.12657
Iteration 2: strain = 594.12657
Modern multidimensional scaling
dissimilarity: L2, computed on 8 variables
Loss criterion: strain = loss for classical MDS
Transformation: identity (no transformation)
Number of obs = 25
Dimensions = 2
Normalization: principal Loss criterion = 594.1266
mds calories-K, id(brand) method(nonmetric) loss(stress) transform(monotonic)
Iteration 1t: stress = .02607533
Iteration 1c: stress = .02115885
(omitted)
Iteration 77t: stress = .01541258
Iteration 77c: stress = .01541258
Modern multidimensional scaling
dissimilarity: L2, computed on 8 variables
Loss criterion: stress = raw_stress/norm(distances)
Transformation: monotonic (nonmetric)
Number of obs = 25
Dimensions = 2
Normalization: principal Loss criterion = 0.0154
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