/* discriminant analysis example in Stata */
/* requires Stata 10 or later */
input y1 y2 y3 grp
19.6 5.15 9.5 1
15.4 5.75 9.1 1
22.3 4.35 3.3 1
...
19.8 2.85 2.3 3
16.5 6.55 3.3 3
17.4 6.60 1.9 3
end
candisc y1 y2 y3, group(grp)
Canonical linear discriminant analysis
| | Like-
| Canon. Eigen- Variance | lihood
Fcn | Corr. value Prop. Cumul. | Ratio F df1 df2 Prob>F
----+---------------------------------+------------------------------------
1 | 0.6866 .891988 0.9942 0.9942 | 0.5258 3.5382 6 56 0.0049 e
2 | 0.0722 .005242 0.0058 1.0000 | 0.9948 .07601 2 29 0.9270 e
---------------------------------------------------------------------------
Ho: this and smaller canon. corr. are zero; e = exact F
Standardized canonical discriminant function coefficients
| function1 function2
-------------+----------------------
y1 | -1.09906 -.2473492
y2 | .0209204 -.7741557
y3 | -1.109885 .5411163
Canonical structure
| function1 function2
-------------+----------------------
y1 | -.4469698 -.5912455
y2 | -.1799598 -.702846
y3 | -.461776 .5722312
Group means on canonical variables
grp | function1 function2
-------------+----------------------
1 | -1.272352 -.0041395
2 | .6829395 -.0824017
3 | .5894128 .0865412
Resubstitution classification summary
+---------+
| Key |
|---------|
| Number |
| Percent |
+---------+
| Classified
True grp | 1 2 3 | Total
-------------+------------------------+-------
1 | 9 0 2 | 11
| 81.82 0.00 18.18 | 100.00
| |
2 | 2 5 4 | 11
| 18.18 45.45 36.36 | 100.00
| |
3 | 2 5 4 | 11
| 18.18 45.45 36.36 | 100.00
-------------+------------------------+-------
Total | 13 10 10 | 33
| 39.39 30.30 30.30 | 100.00
| |
Priors | 0.3333 0.3333 0.3333 |
estat anova
Univariate ANOVA summaries
| Adj.
Variable | Model MS Resid MS Total MS R-sq R-sq F Pr > F
-------------+-------------------------------------------------------------
y1 | 52.924238 293.96544 278.90037 .1526 .0961 2.701 0.0835
y2 | 3.9751512 126.28728 118.64277 .0305 -.0341 .4722 0.6282
y3 | 81.829694 426.3709 404.83707 .161 .1051 2.879 0.0718
---------------------------------------------------------------------------
Number of obs = 33 Model df = 2 Residual df = 30
estat correlations
Pooled within-group correlation matrix
| y1 y2 y3
-------------+------------------------------
y1 | 1.00000
y2 | 0.03400 1.00000
y3 | -0.58689 0.14732 1.00000
estat errorrate
Error rate estimated by error count
| grp
| 1 2 3 | Total
-------------+---------------------------------+----------
Error rate | .1818182 .5454545 .6363636 | .4545455
-------------+---------------------------------+----------
Priors | .3333333 .3333333 .3333333 |
estat grdistance
Mahalanobis squared distances between groups
| grp
grp | 1 2 3
-------------+--------------------------------
1 | 0
2 | 3.829291 0
3 | 3.474393 .037289 0
estat grmeans
Group means
| grp
| 1 2 3
-------------+---------------------------------
y1 | 18.11818 15.52727 15.34545
y2 | 6.190909 5.581818 5.372727
y3 | 8.681818 5.109091 5.636364
estat manova
Number of obs = 33
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
-----------+--------------------------------------------------
grp | W 0.5258 2 6.0 56.0 3.54 0.0049 e
| P 0.4767 6.0 58.0 3.02 0.0122 a
| L 0.8972 6.0 54.0 4.04 0.0021 a
| R 0.8920 3.0 29.0 8.62 0.0003 u
|--------------------------------------------------
Residual | 30
-----------+--------------------------------------------------
Total | 32
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F