Stat Computing > Stata > Textbook Examples > Applied Linear Statistical Models, by Neter, Kutner, Nachtsheim, and Wasserman
Stata Textbook Examples
Applied Linear Statistical Models by Neter, Kutner, et. al.
Chapter 24: Random and Mixed Effects Models
Inputting the Apex Enterprises data
clear input rating officer candidate 76 1 1 65 1 2 85 1 3 74 1 4 59 2 1 75 2 2 81 2 3 67 2 4 49 3 1 63 3 2 61 3 3 46 3 4 74 4 1 71 4 2 85 4 3 89 4 4 66 5 1 84 5 2 80 5 3 79 5 4 end
Table 24.1, p. 964.
table officer candidate, contents(mean rating) col
sum rating
---------------------------------------------
| candidate
officer | 1 2 3 4 Total
----------+----------------------------------
1 | 76 65 85 74 75
2 | 59 75 81 67 70.5
3 | 49 63 61 46 54.75
4 | 74 71 85 89 79.75
5 | 66 84 80 79 77.25
---------------------------------------------
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
rating | 20 71.45 11.87423 46 89
Fig. 24.2, p. 964.
twoway scatter officer rating
Table 24.2, p. 965.
anova rating officer
Number of obs = 20 R-squared = 0.5897
Root MSE = 8.56057 Adj R-squared = 0.4803
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 1579.7 4 394.925 5.39 0.0068
|
officer | 1579.7 4 394.925 5.39 0.0068
|
Residual | 1099.25 15 73.2833333
-----------+----------------------------------------------------
Total | 2678.95 19 140.997368
Estimating the overall mean and calculating the 90% confidence limit, p. 967.
scalar mstr = e(ss_1)/e(df_1) scalar N = r(N) sum rating di "s^2 = " mstr/N di "s = " sqrt(mstr/N) di "t = " invttail(4,.05) di "mean = " r(mean) di "lower = " r(mean)-invttail(n,.05)*sqrt(mstr/N) di "upper = " r(mean)+invttail(n,.05)*sqrt(mstr/N) s^2 = 19.74625 s = 4.4436753 t = 2.1318468 mean = 71.45 lower = 61.976765 upper = 80.923235
Estimating the 90% confidence limit of simga_mu2/(sigma_mu2 + sigma2), p. 968-969.
quietly: anova rating officer scalar mse = e(rmse)^2 scalar mstr = e(ss_1)/e(df_1) scalar n = e(df_1) scalar rbyn = e(df_r) di "L = " (1/n)*((round(mstr,.1)/round(mse,.1))*(1/round(invF(n,rbyn,0.95),.01))-1) di "U = "(1/n)*((round(mstr,.1)/round(mse,.1))*(1/round(invF(n,rbyn,0.05),.01))-1) di "L* = " (1/n)*((round(mstr,.1)/round(mse,.1))*(1/round(invF(n,rbyn,0.95),.01))-1) /// /(1+(1/n)*((round(mstr,.1)/round(mse,.1))*(1/round(invF(n,rbyn,0.95),.01))-1)) di "U* = "(1/n)*((round(mstr,.1)/round(mse,.1))*(1/round(invF(n,rbyn,0.05),.01))-1) /// /(1+(1/n)*((round(mstr,.1)/round(mse,.1))*(1/round(invF(n,rbyn,0.05),.01))-1)) L = .19015105 U = 7.6727189 L* = .15977052 U* = .88469591
Estimating the standard error of sigma2, p. 970.
quietly: anova rating officer scalar mse = e(rmse)^2 scalar rbyn = e(df_r) di "sigma2 L = " rbyn*mse/invchi2(rbyn,.95) di "sigma2 U = " rbyn*mse/invchi2(rbyn,.05) di "sigma L = " sqrt(rbyn*mse/invchi2(rbyn,.95)) di "sigma U = " sqrt(rbyn*mse/invchi2(rbyn,.05)) sigma2 L = 43.977406 sigma2 U = 151.39216 sigma L = 6.6315462 sigma U = 12.304152
Point and interval estimation of sigma_mu2, p. 972-973.
quietly: anova rating officer scalar n = e(df_1) scalar rbyn = e(df_r) scalar mse = e(rmse)^2 scalar mstr = e(ss_1)/n scalar sigma_mu2 = (mstr-mse)/n di "sigma_mu2 = " sigma_mu2 di "df = " (n*sigma_mu2)^2 / ((mstr^2/n)+mse^2/rbyn) di "sigma_mu2 L = " 3*sigma_mu2/invchi2(3,.95) di "sigma_mu2 U = " 3*sigma_mu2/invchi2(3,.05) di "sigma_mu L = " sqrt(3*sigma_mu2/invchi2(3,.95)) di "sigma_mu U = " sqrt(3*sigma_mu2/invchi2(3,.05)) sigma_mu2 = 80.410417 df = 2.6290917 sigma_mu2 L = 30.868797 sigma_mu2 U = 685.61539 sigma_mu L = 5.5559695 sigma_mu U = 26.184258
Interval estimation of sigma_mu2 using the MLS Procedure, p. 974.
quietly: anova rating officer scalar ms1 = round(e(ss_1)/e(df_1),.1) scalar ms2 = round(e(rmse)^2,.1) scalar df1 = e(df_1) scalar df2 = e(df_r) scalar c1 = 1/df1 scalar c2 = -1/df1 scalar sigma_mu2 = round((ms1-ms2)/df1,.1) di "c1=" c1 ", c2=" c2 ", ms1=" ms1 ", ms2=" ms2 ", df1=" df1 ", df2=" df2 ", Lhat=" sigma_mu2 "." scalar f1 = round(invF(df1,10000,.95),.01) scalar f2 = round(invF(df2,10000,.95),.01) scalar f3 = round(invF(10000,df1,.95),.01) scalar f4 = round(invF(10000,df2,.95),.01) scalar f5 = round(invF(df1,df2,.95),.01) scalar f6 = round(invF(df2,df1,.95),.01) di "f1=" f1 ", f2=" f2 ", f3=" f3 ", f4=" f4 ", f5=" f5 ", f6=" f6 "." scalar g1 = round(1-(1/f1),.0001) scalar g2 = round(1 - (1/f2),.0001) scalar g3 = round(((f5-1)^2 - (g1*f5)^2 - (f4-1)^2)/f5,.0001) scalar g4 = round(f6*( ((f6-1)/f6)^2 - ((f3-1)/f6)^2 - g2^2),.0001) di "g1=" g1 ", g2=" g2 ", g3=" g3 ", g4=" g4 "." scalar h_l = ((g1*c1*ms1)^2 + ((f4-1)*c2*ms2)^2 - g3*c1*c2*ms1*ms2)^(1/2) scalar h_u = (((f3-1)*c1*ms1)^2 + (g2*c2*ms2)^2 - g4*c1*c2*ms1*ms2)^(1/2) di "H_l=" h_l ", H_u=" h_u "." di "sigma_mu2 L = " sigma_mu2-h_l di "sigma_mu2 U = " sigma_mu2+h_u di "sigma_mu L = " sqrt(sigma_mu2-h_l) di "sigma_mu U = " sqrt(sigma_mu2+h_u) c1=.25, c2=-.25, ms1=394.9, ms2=73.3, df1=4, df2=15, Lhat=80.4. f1=2.37, f2=1.67, f3=5.63, f4=2.07, f5=3.06, f6=5.86. g1=.5781, g2=.4012, g3=-.01, g4=-.5708. H_l=60.197101, H_u=456.02504. sigma_mu2 L = 20.202899 sigma_mu2 U = 536.42504 sigma_mu L = 4.4947635 sigma_mu U = 23.160851
The training example p. 982-983, 987-988 and 989 was omitted because the data is not available.
Inputting Sheffield Foods Co. data, table 24.11, p. 995.
table rep lab, contents(mean fat) by(method)
----------------------------------
method | lab
and rep | 1 2 3 4
----------+-----------------------
1 |
1 | 5.19 4.09 4.62 3.71
2 | 5.09 3.99 4.32 3.86
3 | 3.75 4.35 3.79
4 | 4.04 4.59 3.63
5 | 4.06
6 |
----------+-----------------------
2 |
1 | 3.26 3.02 3.08 2.98
2 | 3.48 3.32 2.95 2.89
3 | 3.24 2.83 2.98 2.75
4 | 3.41 2.96 2.74 3.04
5 | 3.35 3.23 3.07 2.88
6 | 3.04 3.07 2.7 3.2
----------------------------------
Figure 24.3, p. 995
dotplot fat if method==1, over(lab) name(method1) dotplot fat if method==2, over(lab) name(method2)
Figure 24.4, p. 996.
Note this code uses the user-written program anovaplot, to find and download this program type "findit anovaplot" (without the quotation marks) in the Stata command window.
Table 24.13-24.14 and fig. 24.5 were not generated, p. 1000-1001.
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