Table 8.22 shows fitted values for models for four-way tables that have direct estimates.

a. Use Birch€™s results to verify that the entry is correct for (W, X, Y, Z). Verify its residual df.

b. Motivate the estimate and df formulas for (WX, YZ), (WXY, Z), (WXY, WZ), and (WXY, WXZ) using composite variables and the corresponding results for two-way tables [e.g., for (WXY, WZ), given W, Z is independent of the composite XV variable].

Table 8.22:

Transcribed Image Text:

Expected Frequency Estimate Model Residual DF Пр..п..л..j.п..../n' Пы,п,.j.п.../n* Пы Презь п,../П Пыеп,.j/n (Wх, WY, XZ) ПысьПрејь Пьs/ПревПо (Wх, WY, WZ) пысsпрее Пре../(пр "му-п.../n Пму-П/п,... Пыj- Пыek/Пы* (W, х, Y, Z) (Wх, Y, Z) (WX, WY, Z) HIJK – H -1-J-K+3 HIJK - HI - J - K+ 2 HUK - HI - Н - К +Н+1 ...../п.. (WX, YZ) (HI - 1XJK - 1) HIJK - HI - Н - IК + Н +1 НIIK - HI - Н - НК + 2H (НJ - 1XK - 1) Н(U - 1XK - 1) HI(J - 1XK - 1) (WXY, Z) (WXY, WZ) (иXY, WXZ) "Number of levebs of W, X, Y, Z, deпoted by H, I, J, K. Estimates for other models of cach tуре are obtained by symmetry.