Here is what I thought:

1) Look at the scale of measurement of all the variables. If scales are different, e.g., Height vs age, you should normalize all the variables. Or use correlation matrix.

2) Check each variable, if they are close to normally distributed. Otherwise use transformation. This will ensure that all variables are in the elliptical space.


3) In SAS, here is an example: (using correlation matrix)


A) The data:

 data Crime;
 title 'Crime Rates per 100,000 Population by State';
 input State $1-15 Murder Rape Robbery Assault 
 Burglary Larceny Auto_Theft;
 datalines;
 Alabama 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7
 Alaska 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3
 Arizona 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5
 Arkansas 8.8 27.6 83.2 203.4 972.6 1862.1 183.4
 California 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5
 Colorado 6.3 42.0 170.7 292.9 1935.2 3903.2 477.1
 Connecticut 4.2 16.8 129.5 131.8 1346.0 2620.7 593.2
 Delaware 6.0 24.9 157.0 194.2 1682.6 3678.4 467.0
 Florida 10.2 39.6 187.9 449.1 1859.9 3840.5 351.4
 Georgia 11.7 31.1 140.5 256.5 1351.1 2170.2 297.9
 Hawaii 7.2 25.5 128.0 64.1 1911.5 3920.4 489.4
 Idaho 5.5 19.4 39.6 172.5 1050.8 2599.6 237.6
 Illinois 9.9 21.8 211.3 209.0 1085.0 2828.5 528.6
 Indiana 7.4 26.5 123.2 153.5 1086.2 2498.7 377.4
 Iowa 2.3 10.6 41.2 89.8 812.5 2685.1 219.9
 Kansas 6.6 22.0 100.7 180.5 1270.4 2739.3 244.3
 Kentucky 10.1 19.1 81.1 123.3 872.2 1662.1 245.4
 Louisiana 15.5 30.9 142.9 335.5 1165.5 2469.9 337.7
 Maine 2.4 13.5 38.7 170.0 1253.1 2350.7 246.9
 Maryland 8.0 34.8 292.1 358.9 1400.0 3177.7 428.5
...
;


2) Use the 'PrinComp' procedure:

 proc princomp out=Crime_Components;
 run;

3) Look at the output (results): pay attention to the correlation matirx. If the correlation between two variables close to 1 or -1, you can omit one of them.
 Also pay attention to the eigenvalues of correlation matrix. If eigenvalue < 1 do not use it


 Hope this helps.



Crime Rates per 100,000 Population by State
 
 

The PRINCOMP Procedure

Observations	50
Variables	7

Simple Statistics
	Murder	Rape	Robbery	Assault	Burglary	Larceny	Auto_Theft
Mean	7.444000000	25.73400000	124.0920000	211.3000000	1291.904000	2671.288000	377.5260000
StD	3.866768941	10.75962995	88.3485672	100.2530492	432.455711	725.908707	193.3944175

Correlation Matrix
	Murder	Rape	Robbery	Assault	Burglary	Larceny	Auto_Theft
Murder	1.0000	0.6012	0.4837	0.6486	0.3858	0.1019	0.0688
Rape	0.6012	1.0000	0.5919	0.7403	0.7121	0.6140	0.3489
Robbery	0.4837	0.5919	1.0000	0.5571	0.6372	0.4467	0.5907
Assault	0.6486	0.7403	0.5571	1.0000	0.6229	0.4044	0.2758
Burglary	0.3858	0.7121	0.6372	0.6229	1.0000	0.7921	0.5580
Larceny	0.1019	0.6140	0.4467	0.4044	0.7921	1.0000	0.4442
Auto_Theft	0.0688	0.3489	0.5907	0.2758	0.5580	0.4442	1.0000

Eigenvalues of the Correlation Matrix
	Eigenvalue	Difference	Proportion	Cumulative
1	4.11495951	2.87623768	0.5879	0.5879
2	1.23872183	0.51290521	0.1770	0.7648
3	0.72581663	0.40938458	0.1037	0.8685
4	0.31643205	0.05845759	0.0452	0.9137
5	0.25797446	0.03593499	0.0369	0.9506
6	0.22203947	0.09798342	0.0317	0.9823
7	0.12405606		0.0177	1.0000

Eigenvectors
	Prin1	Prin2	Prin3	Prin4	Prin5	Prin6	Prin7
Murder	0.300279	-.629174	0.178245	-.232114	0.538123	0.259117	0.267593
Rape	0.431759	-.169435	-.244198	0.062216	0.188471	-.773271	-.296485
Robbery	0.396875	0.042247	0.495861	-.557989	-.519977	-.114385	-.003903
Assault	0.396652	-.343528	-.069510	0.629804	-.506651	0.172363	0.191745
Burglary	0.440157	0.203341	-.209895	-.057555	0.101033	0.535987	-.648117
Larceny	0.357360	0.402319	-.539231	-.234890	0.030099	0.039406	0.601690
Auto_Theft	0.295177	0.502421	0.568384	0.419238	0.369753	-.057298	0.147046

主成分分析中得出的主成分只是原始指标的线性组合，即载荷矩阵，要实现主成分与原始指标的关联，还需要对载荷矩阵进行因子旋转，得出公共因子，有的时候并不一定得出结论。请参考人大出版社出版的《多元统计分析》何晓群编著，有主成分分析因子分析的上机实现(spss)很详细，在SPSS中主成分分析和因子分析是结合在一起的