SAS discriminant analysis (Bayes criterion and proc discrim process)

The following table shows the relevant financial data of the two types of companies , One is a bankrupt company , The data in the table are the four-year financial indicators of these companies in the two years before bankruptcy . One is the four same financial indicators of the non bankrupt company and the bankrupt company in the same period . These four indicators are

  The data of each company is shown in the following table （ In the last column of the table “0” Means bankrupt company ,“1” Means a non bankrupt company ）

number	x1	x2	x3	x4	group
1	-0.45	-0.41	1.09	0.45	0
2	-0.56	-0.31	1.51	0.16	0
3	0.06	0.02	1.01	0.4	0
4	-0.07	-0.09	1.45	0.26	0
5	-0.1	-0.09	1.56	0.67	0
6	-0.14	-0.07	0.71	0.28	0
7	0.04	0.01	1.5	0.71	0
8	-0.06	-0.06	1.37	0.4	0
9	0.07	-0.01	1.37	0.34	0
10	-0.13	-0.14	1.42	0.44	0
11	-0.23	-0.3	0.33	0.18	0
12	0.07	0.02	1.31	0.25	0
13	0.01	0	2.15	0.7	0
14	-0.28	-0.23	1.19	0.66	0
15	0.15	0.05	1.88	0.27	0
16	0.37	0.11	1.99	0.38	0
17	-0.08	-0.08	1.51	0.42	0
18	0.05	0.03	1.68	0.95	0
19	0.01	0	1.26	0.6	0
20	0.12	0.11	1.14	0.17	0
21	-0.28	-0.27	1.27	0.51	0
1	0.51	0.1	2.49	0.54	1
2	0.08	0.02	2.01	0.53	1
3	0.38	0.11	3.27	0.35	1
4	0.19	0.05	2.25	0.33	1
5	0.32	0.07	4.24	0.63	1
6	0.31	0.05	4.45	0.69	1
7	0.12	0.05	2.52	0.69	1
8	-0.02	0.02	2.05	0.35	1
9	0.22	0.08	2.35	0.4	1
10	0.17	0.07	1.8	0.52	1
11	0.15	0.05	2.17	0.55	1
12	-0.1	-0.01	2.5	0.58	1
13	0.14	-0.03	0.46	0.26	1
14	0.14	0.07	2.61	0.52	1
15	0.15	0.06	2.23	0.56	1
16	0.16	0.05	2.31	0.2	1
17	0.29	0.06	1.84	0.38	1
18	0.54	0.11	2.33	0.48	1
19	-0.33	-0.09	3.01	0.47	1
20	0.48	0.09	1.24	0.18	1
21	0.56	0.11	4.29	0.45	1
22	0.2	0.08	1.99	0.3	1
23	0.47	0.16	2.92	0.45	1
24	0.17	0.04	2.45	0.14	1
25	0.58	0.04	5.06	0.13	1

  Experimental code ：

proc import out=temp1                                                                                                                   
datafile="C:\Users\86166\Desktop\IT\SAS experiment \ experiment 9\1.xls"                                                                                
DBMS=EXCEL2000 replace;                                                                                                                 
run;   

/*1、2、3*/ 
proc discrim data=temp1  wcov simple pool=no manova method=normal crosslisterr listerr;
class group;
var x1-x2;
priors equal;
run;
/*4*/
proc discrim data=temp1  pool=no manova method=normal crosslisterr listerr;
class group;
var x1-x2;
priors '0'=0.05 '1'=0.95;
run;
/*5*/ 
proc discrim data=temp1  pool=yes manova method=normal crosslisterr listerr;
class group;
var x1-x2;
priors equal;
run;
/*6*/
proc discrim data=temp1  wcov simple pool=no manova method=normal crosslisterr listerr;
class group;
var x1 x3;
priors equal;
run;
proc discrim data=temp1  pool=no manova method=normal crosslisterr listerr;
class group;
var x1 x3;
priors '0'=0.05 '1'=0.95;
run;

proc discrim data=temp1  wcov simple pool=no manova method=normal crosslisterr listerr;
class group;
var x1 x4;
priors equal;
run;
proc discrim data=temp1  pool=no manova method=normal crosslisterr listerr;
class group;
var x1 x4;
priors '0'=0.05 '1'=0.95;
run;
/*7*/ 
proc discrim data=temp1  wcov simple pool=no manova method=normal crosslisterr listerr;
class group;
var x1-x4;
priors equal;
run;
proc discrim data=temp1  pool=no manova method=normal crosslisterr listerr;
class group;
var x1-x4;
priors '0'=0.05 '1'=0.95;
run;

experimental result ：——》 Discriminant analysis code picture results and data sets

Analyze the results of the experiment ：

Problems and solutions in the experiment ：

problem ： How to determine the more reliable results under different prior probabilities ？

solve ： At present, the error probability is directly used to compare

Experimental experience （ Conclusion 、 evaluation 、 Thoughts and suggestions ）

1. simple Obtain simple statistics such as the mean ,wcov Get intra group covariance ,pool=yes/no/test Use the joint covariance matrix respectively , Intra group covariance matrix , Homogeneity test of intra group covariance matrix .manova obtain 4 Statistics ,Wilks'lambda To measure The ratio of the sum of squares within the group to the total sum of squares ,Wilks'lambda Large value , It means that the mean value of each group is basically the same , In discriminant analysis , Only when the group mean values are not equal , Discriminant analysis makes sense .
2. crosslisterr listerr Maximum a posteriori probabilities are used respectively , Calculate the probability of misjudgment by cutting ,method=normal Specifies that the population is normally distributed ,priors equal Specifies that the prior probability is equal , The prior probabilities of different classes can also be specified according to the contents of the classification .
3. When the population is normally distributed , If covariance matrix between populations is not equal , The intra group covariance matrix ,pool=no,method=normal,priors Can be equal to , It can also be specified by frequency or special value ; If covariance matrix between populations is equal , Then the joint covariance matrix ,pool=yes,method=normal,priors Can be equal to , It can also be specified by frequency or special value . Joint covariance matrix is preferred for small samples , A priori probability generally specifies equality . When the population does not belong to the normal distribution method=npar, The nonparametric method is used for discrimination .
4. The mean vectors of the population and each class can be represented by simple obtain
   wcov Get the intra group covariance , That is, the sample covariance
   pcov Get the combined covariance , The corresponding use conditions of these two covariances are pool relation
   pool by yes The combined covariance matrix , It means that the corresponding overall covariance matrix is different
   by no The intra group covariance matrix , It means that the corresponding populations obey the normal population with equal covariance matrix
   by test The likelihood ratio test for homogeneity of the intra group covariance matrix is modified , and slpool Used to specify the homogeneity inspection level , Default 0.1
   method by normal The representation class obeys multivariate normal distribution , by npar That is, the nonparametric method is used to disobey the distribution
   crosslisterr Output the back judgment result in the form of cross table , The knife cutting method is used
   listerr The back decision error information generated by a posteriori probability , It is required to obtain the discrimination result according to the distance criterion
   priors by equal Means that the prior probabilities are equal , by proportional Means that the prior probability is equal to the sample frequency , You can also specify a priori probability of the classification mark , But the sum is 1
   Compare the quality of the criterion , Look at the result of misjudgment Total Options , Generally speaking, whoever is smaller is better