???,?X=(x1, x2,

1
????

• ??????

2
????

• ??????
• ?????
• ??????????????????????

3
????????

• ???,?X(x1, x2, ,xp)?????????,??
• f(f1,f2,,fm)???(??)??(common
  factor),????(factor)

4

• e(e1,e2,,ep)?????(specific factor)
• f?e?????????????
• µ(µ1,µ2,,µp)?????x?????
• A(aij)pm?????(??)(factor loading)??

5

• ????x??????,??????????????,???1.????
• ??(1)fi????0,???1
• (2)ei????0,???di
• (3) fi?ei????.
• ??x???m??????????

6

• ?????(4)fi?fj????(i?j),???????????????
• ????????????
• x???????
• ?

7

• (1)hi2?m???????i??????,???i????(communality)?????,
  ?????(common variance)
• (2)di??????(specific variance),?????????????

8

• ????(??)aij?????xi?????fj??????
• ?
• ?gj2?????fj?x???,???????fj?????????

9
?????????

• ??????xnp,?????????,???????(??)
• ?????????R(rij)pp
• ????????????i (?1,?2,,?pgt0)?????????????li

10

• ???????
• ???????????hi2
• ?????????,????????????
• ??????????????

11
?????????????

• ????(principal component factor)

12

• ????????????????????????,??????????

13

• ?????(maximum likelihood factor)
• ???????????,????????????????,????????????????,??
  ??,??????

14

• ????(principal factor)
• ??????????R(rij),?????R-1(rij)???????????????
  ????????????,di1/rii??????????(hi)21-
  di1-1/rii?

15

• ?(hi)2???????????????,?????????
• (h1)2 r12 r1p
• r21 (h2)2 r2p
• R . . .
• . . .
• rp1 rp2 (hp)2
• R??m???????????????????????

16

• ??????(iterated principal factor)
• ????????????,????????????,????????,????????????
  ?,????????????????????????,??????????????????,????
  ????

17

• Heywood??
• ????

18
??????

• ???????????,?????0,?????1?
• ???????

19

• (1)????????
• (varimax orthogonal rotation)
• ??????????????(lij/hi2)???????,??????????????????
  ????
• ????????????????????,?????????????

20

• (2)????(oblique rotation)
• ???????,????????????,??????????????????,??????????
  ????????????????
• ?????????????

21
??????

• Thomson?,????
• ???????Bayes?????,???????????,??????????

22

• Bartlett?
• Bartlett???????????,??????????,???????????,????
  ??????
• ???????????,???????????????

23
??????????
24
?????????????

• ????
• (1)??????,????????(Pearson??????)???????????
• (2)??????

25

• ???
• ???????????????????????
• ????
• ????,???????80???????Heywood???

26

• ??!