Question: Table 8.22 shows fitted values for models for four-way tables that have direct estimates. a. Use Birchs results to verify that the entry is correct

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:

Expected Frequency Estimate Model Residual DF Пр..п..л..j.п..../n' Пы,п,.j.п.../n* Пы Презь п,../П П?

Expected Frequency Estimate Model Residual DF ......j...../n' ,,.j..../n* ,../ ,.j/n (W, WY, XZ) s/ (W, WY, WZ) s ../( "-.../n -/,... j- ek/* (W, , Y, Z) (W, Y, Z) (WX, WY, Z) HIJK H -1-J-K+3 HIJK - HI - J - K+ 2 HUK - HI - - ++1 ...../.. (WX, YZ) (HI - 1XJK - 1) HIJK - HI - - I + +1 IIK - HI - - + 2H (J - 1XK - 1) (U - 1XK - 1) HI(J - 1XK - 1) (WXY, Z) (WXY, WZ) (XY, WXZ) "Number of levebs of W, X, Y, Z, deoted by H, I, J, K. Estimates for other models of cach t are obtained by symmetry.

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