Nested ANOVA for fecundity

Data simulated from Cronin and Strong (1996)

Obs site isoline wasp eggs y site_jit
1 1 1 1 37 37 0.87730
2 1 1 2 41 41 1.04063
3 1 1 3 46 46 0.91527
4 1 1 4 44 44 0.85992
5 1 1 5 43 43 0.95591
6 1 1 6 41 41 1.04877
7 1 1 7 38 38 0.97793
8 1 1 8 37 37 0.90332
9 1 2 1 37 37 1.06790
10 1 2 2 28 28 1.08741
11 1 2 3 34 34 0.88534
12 1 2 4 37 37 0.97417
13 1 2 5 35 35 1.01558
14 1 2 6 39 39 1.02913
15 1 2 7 36 36 1.07770
16 1 2 8 29 29 1.15744
17 1 3 1 35 35 0.96031
18 1 3 2 37 37 0.99451
19 1 3 3 40 40 1.05269
20 1 3 4 39 39 1.00900
21 1 3 5 37 37 1.03514
22 1 3 6 44 44 0.98718
23 1 3 7 35 35 1.21997
24 1 3 8 38 38 1.08533
25 1 4 1 28 28 0.88047
26 1 4 2 36 36 0.95910
27 1 4 3 31 31 0.98881
28 1 4 4 27 27 0.91150
29 1 4 5 36 36 0.93099
30 1 4 6 33 33 0.93033
31 1 4 7 31 31 1.00863
32 1 4 8 35 35 1.03552
33 1 5 1 34 34 1.05070
34 1 5 2 35 35 1.04845
35 1 5 3 30 30 0.99655
36 1 5 4 39 39 0.94536
37 1 5 5 42 42 0.97780
38 1 5 6 39 39 0.90088
39 1 5 7 38 38 1.04766
40 1 5 8 32 32 1.06567
41 1 6 1 30 30 1.14520
42 1 6 2 32 32 1.16601
43 1 6 3 35 35 0.97777
44 1 6 4 35 35 1.06487
45 1 6 5 32 32 0.92253
46 1 6 6 31 31 0.93206
47 1 6 7 34 34 0.90961
48 1 6 8 30 30 0.99031
49 1 7 1 30 30 0.99137
50 1 7 2 36 36 1.09753
51 1 7 3 37 37 0.88910
52 1 7 4 30 30 1.06653
53 1 7 5 41 41 0.86493
54 1 7 6 35 35 1.02039
55 1 7 7 34 34 1.03080
56 1 7 8 37 37 1.00402
57 1 8 1 25 25 0.92245
58 1 8 2 31 31 1.00395
59 1 8 3 24 24 0.95410
60 1 8 4 26 26 0.89291
61 1 8 5 30 30 0.90930
62 1 8 6 31 31 0.97673
63 1 8 7 25 25 1.02216
64 1 8 8 24 24 0.99739
65 1 9 1 34 34 0.94926
66 1 9 2 35 35 1.01954
67 1 9 3 29 29 1.11965
68 1 9 4 34 34 1.02111
69 1 9 5 34 34 0.95977
70 1 9 6 40 40 1.06618
71 1 9 7 37 37 1.01303
72 1 9 8 37 37 1.04265
73 1 10 1 38 38 0.98086
74 1 10 2 30 30 1.19981
75 1 10 3 33 33 1.03659
76 1 10 4 32 32 1.04574
77 1 10 5 33 33 0.85406
78 1 10 6 34 34 1.04971
79 1 10 7 35 35 1.20233
80 1 10 8 41 41 1.08777
81 1 11 1 36 36 0.85452
82 1 11 2 33 33 1.02460
83 1 11 3 36 36 0.84747
84 1 11 4 34 34 0.87215
85 1 11 5 37 37 0.89804
86 1 11 6 41 41 0.93072
87 1 11 7 37 37 0.96577
88 1 11 8 31 31 0.98029
89 1 12 1 35 35 0.92723
90 1 12 2 36 36 1.08372
91 1 12 3 35 35 1.01714
92 1 12 4 37 37 1.13967
93 1 12 5 40 40 1.04519
94 1 12 6 34 34 1.00529
95 1 12 7 29 29 0.99110
96 1 12 8 42 42 0.90972
97 1 13 1 33 33 0.88808
98 1 13 2 39 39 0.95392
99 1 13 3 33 33 1.08781
100 1 13 4 37 37 0.82418
101 1 13 5 28 28 1.07746
102 1 13 6 35 35 1.06910
103 1 13 7 34 34 1.01884
104 1 13 8 38 38 1.13941
105 1 14 1 35 35 0.92431
106 1 14 2 33 33 0.86292
107 1 14 3 25 25 0.99359
108 1 14 4 29 29 0.94661
109 1 14 5 29 29 0.97996
110 1 14 6 35 35 0.98880
111 1 14 7 33 33 1.10456
112 1 14 8 29 29 0.86320
113 2 1 1 26 26 2.02973
114 2 1 2 39 39 2.19847
115 2 1 3 36 36 2.04032
116 2 1 4 27 27 1.98783
117 2 1 5 25 25 1.90049
118 2 1 6 31 31 2.11500
119 2 1 7 30 30 1.88428
120 2 1 8 25 25 1.91311
121 2 2 1 42 42 1.89795
122 2 2 2 46 46 2.08522
123 2 2 3 46 46 2.00596
124 2 2 4 42 42 2.01855
125 2 2 5 43 43 1.81359
126 2 2 6 36 36 1.98729
127 2 2 7 36 36 2.00889
128 2 2 8 41 41 2.16042
129 2 3 1 38 38 2.06768
130 2 3 2 36 36 1.93002
131 2 3 3 35 35 2.06709
132 2 3 4 31 31 2.18950
133 2 3 5 36 36 2.09637
134 2 3 6 32 32 1.98082
135 2 3 7 29 29 1.99857
136 2 3 8 34 34 1.77619
137 2 4 1 28 28 2.02758
138 2 4 2 36 36 1.85778
139 2 4 3 33 33 2.13445
140 2 4 4 32 32 2.05222
141 2 4 5 27 27 1.97664
142 2 4 6 31 31 1.91606
143 2 4 7 30 30 2.03577
144 2 4 8 32 32 1.83613
145 2 5 1 30 30 1.88781
146 2 5 2 35 35 2.05454
147 2 5 3 32 32 1.86861
148 2 5 4 31 31 2.01895
149 2 5 5 36 36 1.81219
150 2 5 6 34 34 2.03922
151 2 5 7 29 29 2.07490
152 2 5 8 36 36 1.95965
153 2 6 1 28 28 2.04528
154 2 6 2 34 34 2.01831
155 2 6 3 34 34 1.99660
156 2 6 4 35 35 1.86598
157 2 6 5 32 32 2.09099
158 2 6 6 31 31 1.99669
159 2 6 7 24 24 2.06007
160 2 6 8 31 31 1.98811
161 2 7 1 35 35 1.95497
162 2 7 2 34 34 1.97088
163 2 7 3 44 44 2.10150
164 2 7 4 34 34 2.00620
165 2 7 5 35 35 2.01342
166 2 7 6 36 36 1.83114
167 2 7 7 32 32 2.00197
168 2 7 8 30 30 2.06835
169 2 8 1 37 37 1.84159
170 2 8 2 32 32 2.08707
171 2 8 3 33 33 2.06187
172 2 8 4 39 39 1.90608
173 2 8 5 30 30 2.14981
174 2 8 6 31 31 2.03568
175 2 8 7 32 32 2.15432
176 2 8 8 34 34 2.04923
177 2 9 1 41 41 2.18868
178 2 9 2 41 41 1.95221
179 2 9 3 43 43 1.87008
180 2 9 4 36 36 1.98877
181 2 9 5 43 43 2.06159
182 2 9 6 42 42 1.99026
183 2 9 7 42 42 2.00407
184 2 9 8 37 37 1.94470
185 2 10 1 34 34 2.04338
186 2 10 2 30 30 1.94891
187 2 10 3 35 35 2.11807
188 2 10 4 27 27 2.02394
189 2 10 5 30 30 2.05745
190 2 10 6 22 22 1.90769
191 2 10 7 31 31 1.93620
192 2 10 8 31 31 1.95271
193 2 11 1 34 34 2.00733
194 2 11 2 36 36 1.92104
195 2 11 3 38 38 2.00976
196 2 11 4 36 36 2.00176
197 2 11 5 34 34 1.97761
198 2 11 6 33 33 2.03771
199 2 11 7 35 35 2.14544
200 2 11 8 29 29 1.99533
201 2 12 1 28 28 1.98932
202 2 12 2 29 29 2.09829
203 2 12 3 27 27 1.85719
204 2 12 4 36 36 1.76839
205 2 12 5 33 33 1.92741
206 2 12 6 32 32 1.87321
207 2 12 7 34 34 1.95943
208 2 12 8 32 32 2.04771
209 2 13 1 40 40 2.05026
210 2 13 2 39 39 2.07749
211 2 13 3 39 39 1.87952
212 2 13 4 34 34 1.96802
213 2 13 5 32 32 2.03177
214 2 13 6 42 42 2.06229
215 2 13 7 36 36 2.04931
216 2 13 8 39 39 1.90282
217 2 14 1 38 38 1.93440
218 2 14 2 42 42 2.18288
219 2 14 3 37 37 2.10028
220 2 14 4 37 37 1.96047
221 2 14 5 34 34 2.05063
222 2 14 6 33 33 1.98494
223 2 14 7 43 43 2.10120
224 2 14 8 34 34 1.86937
225 3 1 1 30 30 3.00340
226 3 1 2 35 35 2.91010
227 3 1 3 36 36 2.97836
228 3 1 4 37 37 3.12117
229 3 1 5 29 29 3.04407
230 3 1 6 27 27 3.03900
231 3 1 7 39 39 3.18953
232 3 1 8 38 38 3.01189
233 3 2 1 30 30 3.02108
234 3 2 2 37 37 3.03850
235 3 2 3 30 30 2.82062
236 3 2 4 31 31 2.99455
237 3 2 5 27 27 3.05776
238 3 2 6 31 31 2.98883
239 3 2 7 36 36 3.07019
240 3 2 8 40 40 3.09037
241 3 3 1 27 27 3.17878
242 3 3 2 33 33 3.16195
243 3 3 3 31 31 3.16021
244 3 3 4 32 32 2.91548
245 3 3 5 34 34 2.92910
246 3 3 6 31 31 2.95602
247 3 3 7 31 31 3.13108
248 3 3 8 31 31 2.98066
249 3 4 1 26 26 3.17919
250 3 4 2 27 27 3.03851
251 3 4 3 37 37 3.00129
252 3 4 4 30 30 2.99240
253 3 4 5 29 29 3.12205
254 3 4 6 35 35 3.10828
255 3 4 7 34 34 2.94642
256 3 4 8 31 31 3.04535
257 3 5 1 36 36 2.95493
258 3 5 2 32 32 3.07091
259 3 5 3 34 34 2.94622
260 3 5 4 37 37 3.01994
261 3 5 5 32 32 2.79654
262 3 5 6 34 34 2.86847
263 3 5 7 33 33 2.97123
264 3 5 8 32 32 2.88027
265 3 6 1 33 33 2.97261
266 3 6 2 40 40 3.11604
267 3 6 3 34 34 2.89949
268 3 6 4 38 38 2.94078
269 3 6 5 36 36 2.99263
270 3 6 6 35 35 3.09022
271 3 6 7 41 41 3.02176
272 3 6 8 34 34 2.90442
273 3 7 1 31 31 2.87179
274 3 7 2 33 33 2.93843
275 3 7 3 31 31 3.03776
276 3 7 4 34 34 2.94615
277 3 7 5 29 29 3.05733
278 3 7 6 33 33 3.05475
279 3 7 7 28 28 3.22903
280 3 7 8 33 33 2.75629
281 3 8 1 22 22 2.98485
282 3 8 2 25 25 3.04113
283 3 8 3 29 29 2.99314
284 3 8 4 24 24 2.93611
285 3 8 5 24 24 3.02249
286 3 8 6 26 26 2.80694
287 3 8 7 25 25 2.94360
288 3 8 8 21 21 3.01899
289 3 9 1 32 32 3.08541
290 3 9 2 31 31 2.91631
291 3 9 3 28 28 3.02633
292 3 9 4 28 28 3.01580
293 3 9 5 35 35 3.06828
294 3 9 6 34 34 2.89799
295 3 9 7 33 33 2.93320
296 3 9 8 31 31 3.00909
297 3 10 1 31 31 3.23076
298 3 10 2 32 32 2.91108
299 3 10 3 29 29 2.92253
300 3 10 4 30 30 2.88013
301 3 10 5 28 28 3.02740
302 3 10 6 31 31 3.16316
303 3 10 7 28 28 3.10456
304 3 10 8 36 36 3.09916
305 3 11 1 32 32 2.87871
306 3 11 2 31 31 3.11946
307 3 11 3 34 34 3.13851
308 3 11 4 35 35 3.01731
309 3 11 5 35 35 2.96874
310 3 11 6 31 31 2.94064
311 3 11 7 41 41 3.11503
312 3 11 8 34 34 3.07764
313 3 12 1 28 28 3.29717
314 3 12 2 27 27 3.05052
315 3 12 3 27 27 2.99760
316 3 12 4 27 27 3.11538
317 3 12 5 27 27 3.01191
318 3 12 6 30 30 2.90802
319 3 12 7 28 28 2.96791
320 3 12 8 28 28 3.01817
321 3 13 1 36 36 3.16995
322 3 13 2 39 39 3.06349
323 3 13 3 36 36 3.09703
324 3 13 4 30 30 3.05460
325 3 13 5 37 37 3.00512
326 3 13 6 32 32 2.89814
327 3 13 7 38 38 3.17230
328 3 13 8 39 39 3.10805
329 3 14 1 32 32 3.12995
330 3 14 2 34 34 3.04234
331 3 14 3 41 41 2.97538
332 3 14 4 33 33 2.93399
333 3 14 5 35 35 2.90107
334 3 14 6 35 35 3.03608
335 3 14 7 34 34 3.10396
336 3 14 8 31 31 2.92219
Nested ANOVA for fecundity; Data simulated from Cronin and Strong 1996; Plot of y by site y 20 30 40 50 site 1 2 3 Nested ANOVA for fecundity Data simulated from Cronin and Strong (1996)
Nested ANOVA for fecundity; Data simulated from Cronin and Strong 1996; Plot of y by site_jit identified by isoline y 20 30 40 50 site_jit 0 1 2 3 4 Nested ANOVA for fecundity Data simulated from Cronin and Strong (1996) isoline 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Nested ANOVA for fecundity

Data simulated from Cronin and Strong (1996)

The Mixed Procedure

Model Information
Data Set WORK.ANAGRUS
Dependent Variable y
Covariance Structure Variance Components
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Kenward-Roger
Degrees of Freedom Method Kenward-Roger
Class Level Information
Class Levels Values
site 3 1 2 3
isoline 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Dimensions
Covariance Parameters 2
Columns in X 4
Columns in Z 42
Subjects 1
Max Obs per Subject 336
Number of Observations
Number of Observations Read 336
Number of Observations Used 336
Number of Observations Not Used 0
Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 1965.68443676  
1 1 1841.14730382 0.00000000
Convergence criteria met.
Covariance Parameter Estimates
Cov Parm Estimate Alpha Lower Upper
isoline(site) 10.1664 0.05 6.5003 18.1260
Residual 11.0187 0.05 9.4338 13.0417
Fit Statistics
-2 Res Log Likelihood 1841.1
AIC (Smaller is Better) 1845.1
AICC (Smaller is Better) 1845.2
BIC (Smaller is Better) 1848.6
Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
site 2 39 2.13 0.1323
Least Squares Means
Effect site Estimate Standard
Error		 DF t Value Pr > |t| Alpha Lower Upper
site 1 34.4821 0.9081 39 37.97 <.0001 0.05 32.6454 36.3188
site 2 34.2946 0.9081 39 37.77 <.0001 0.05 32.4579 36.1313
site 3 32.0982 0.9081 39 35.35 <.0001 0.05 30.2615 33.9349
Differences of Least Squares Means
Effect site _site Estimate Standard
Error		 DF t Value Pr > |t| Adjustment Adj P Alpha Lower Upper Adj Lower Adj Upper
site 1 2 0.1875 1.2842 39 0.15 0.8847 Tukey 0.9883 0.05 -2.4100 2.7850 -2.9411 3.3161
site 1 3 2.3839 1.2842 39 1.86 0.0710 Tukey 0.1651 0.05 -0.2136 4.9814 -0.7447 5.5126
site 2 3 2.1964 1.2842 39 1.71 0.0951 Tukey 0.2142 0.05 -0.4011 4.7939 -0.9322 5.3251
Nested ANOVA for fecundity; Data simulated from Cronin and Strong 1996; Panel of conditional residuals for y. The panel consists of a scatterplot of the residuals, a histogram with normal density, a Q-Q plot, and summary statistics for the residuals and the model fit. Conditional Residuals for y BIC 1848.6 AICC 1845.2 AIC 1845.1 Objective 1841.1 Fit Statistics Std Dev 3.1342 Maximum 9.0842 Mean 21E-16 Minimum -8.512 Observations 336 Residual Statistics -3 -2 -1 0 1 2 3 Quantile -10 -5 0 5 10 Residual -9 -6 -3 0 3 6 9 Residual 0 5 10 15 20 Percent 25 30 35 40 Predicted -10 -5 0 5 10 Residual