Hello,
I have a dataset with the following variables: ID (person's ID number), LPA_Daily_min (daily light physical activity in minutes), ST_win (screen time in hours/day), Errors (number of errors on a cognitive test), Female (gender=female), Location (1-5), and Income_thresh (0, no; 1, yes). The aim is to predict Errors from LPA_Daily_min using regression while adjusting for ST_win, Female, Location, and Income_thresh. Data are below:
data forSas;
input ID LPA_Daily_min ST_win Errors Female Location Income_thresh;
datalines;
1 139.5225 5.5 3 1 1 1
2 139.5225 6.8571 4 0 1 1
3 62.8618266 5.9643 7 0 1 0
4 118.5685101 6.8214 4 0 1 0
5 78.705 6.9286 1 0 1 1
6 88.9264899 7.2857 0 0 1 0
7 65.9281734 8.7857 5 0 1 1
8 10.7325 10.6071 3 0 1 0
9 53.6625 7.25 1 1 1 1
10 64.9060101 7.8571 6 1 1 0
11 114.48 7.6429 2 1 1 0
12 56.2178367 8 0 0 1 1
13 63.3728367 8.0714 7 1 1 1
14 96.5925 6.1429 2 1 1 0
15 107.8360101 7.2143 1 0 1 1
16 50.085 6.7857 4 0 1 1
17 17.3764899 8.8929 1 0 1 1
18 35.775 6.3214 0 1 1 1
19 60.8175 6 4 0 1 0
20 38.8414899 8 1 0 1 1
21 10.7325 6.6429 1 0 2 1
22 96.5925 8.2143 3 1 2 0
23 55.7068266 6.0714 0 1 2 1
24 96.5925 7.2857 5 0 2 0
25 32.1975 7.5714 4 0 2 0
26 55.1956734 6.5714 3 1 2 0
27 51.1071633 6.1429 10 0 2 1
28 47.5296633 7.5357 0 0 2 0
29 60.8175 6.9643 8 0 2 0
30 74.6164899 7.1429 2 1 2 0
31 57.7510101 6.5 0 1 2 1
32 88.9264899 5.9286 8 1 2 1
33 96.5925 4.5 1 0 2 0
34 75.1275 7.5357 2 0 2 0
35 28.62 6.8214 7 1 2 0
36 94.5481734 7.0357 2 0 2 0
37 96.5925 5.8571 9 0 2 1
38 139.5225 4.9286 2 1 2 1
39 96.5925 7.3571 9 0 2 1
40 93.5260101 7.8571 6 1 2 1
41 92.5039899 5.4286 1 0 2 1
42 48.5518266 8.4643 7 0 2 1
43 101.1921633 5.2143 2 1 2 1
44 118.5685101 5.9643 16 0 2 0
45 71.0389899 6.3571 9 0 2 1
46 44.9743266 4.9286 0 0 2 1
47 63.8839899 6.2857 2 0 2 0
48 121.635 6.3571 1 1 2 1
49 93.015 6.4643 3 1 2 1
50 25.0425 8.2143 4 1 2 1
51 17.8875 7.2143 0 0 2 1
52 96.5925 4.6429 6 0 2 0
53 55.1956734 5.1786 12 0 2 0
54 28.1089899 7.6786 5 0 2 0
55 89.4375 5.0714 1 0 2 0
56 31.6864899 4.8214 0 1 2 0
57 71.0389899 8.7143 4 0 2 1
58 101.1921633 7.5357 17 0 2 1
59 93.5260101 5.25 8 1 2 1
60 83.8156734 7.7857 8 0 2 1
61 127.2568266 5.7857 3 0 2 1
62 75.1275 5 3 0 2 1
63 101.7031734 7.6429 0 0 2 1
64 50.085 9.7857 13 0 2 1
65 139.5225 6.8214 0 1 2 0
66 106.3028367 7.2857 1 1 2 1
67 85.86 6.5357 0 0 2 1
68 113.9689899 8.3929 14 0 2 1
69 12.7768266 6 2 0 2 0
70 29.6421633 7.2857 1 1 2 1
71 55.7068266 6.8929 2 0 2 1
72 60.8175 7.5714 0 1 2 1
73 54.1735101 6 0 1 2 0
74 78.705 4.0714 2 1 2 0
75 34.7528367 6.6071 1 0 2 1
76 32.7085101 4.6786 27 0 2 1
77 50.085 8.1786 6 1 2 1
78 100.6810101 7.8214 7 0 3 1
79 139.5225 5.5 2 1 3 1
80 38.8414899 8.7857 1 1 3 1
81 81.2603367 8 10 0 3 1
82 39.8635101 8.6429 3 1 3 1
83 59.7953367 3.4286 1 0 3 0
84 78.705 7.3571 0 1 3 1
85 17.8875 7.2143 6 0 3 0
86 60.8175 7.7857 0 0 3 0
87 110.3914899 7.5714 7 0 3 1
88 30.6643266 9.6429 3 0 3 1
89 25.5535101 7.5 1 0 3 1
90 56.7289899 7.4286 24 0 3 1
91 38.3303367 7.8571 0 0 3 1
92 46.5075 6.5 1 0 3 1
93 106.8139899 7.25 0 0 3 0
94 113.9689899 7.5 3 1 3 1
95 128.79 6.25 13 1 3 1
96 53.1514899 8.8214 0 1 3 1
97 94.5481734 5.5 5 1 3 0
98 32.7085101 10.4286 3 1 3 1
99 88.4153367 8.25 1 1 3 1
100 26.0646633 7.3929 2 1 3 1
101 16.8653367 5.4643 7 0 3 1
102 88.9264899 5.8214 5 1 3 1
103 30.6643266 6.6071 2 0 3 1
104 40.3746633 7.1071 3 0 3 1
105 17.8875 9 2 0 3 1
106 78.705 8.75 10 1 3 0
107 63.8839899 7.1071 2 0 3 1
108 110.3914899 6.5 2 1 3 1
109 121.1239899 7.2857 1 1 3 1
110 57.7510101 7.7857 3 0 3 1
111 35.775 6.8571 2 0 3 1
112 114.48 7.7143 2 1 3 1
113 50.5960101 8.8571 0 0 3 0
114 36.2860101 7.2857 8 0 3 1
115 79.2160101 6.0714 4 0 3 0
116 89.4375 7.8214 2 1 3 1
117 88.4153367 6.9643 1 1 3 1
118 19.9318266 7.7143 2 0 3 1
119 96.5925 8.4286 4 0 3 1
120 96.5925 8.2857 5 0 3 1
121 81.7714899 8.5357 0 1 3 1
122 139.5225 8.8571 1 0 3 1
123 45.4853367 8.8571 0 1 3 1
124 50.085 7.3214 7 0 3 0
125 96.5925 7.6429 3 0 3 1
126 45.9964899 5.7857 3 1 3 0
127 96.5925 8.3214 0 1 3 1
128 65.4171633 7.5714 3 0 3 1
129 71.0389899 6.2857 7 1 3 1
130 96.5925 7.2143 1 0 3 1
131 95.0593266 7.5 0 0 3 1
132 87.9043266 10.6071 2 0 3 1
133 78.705 8.2143 4 0 3 1
134 84.8378367 5.3571 2 1 3 0
135 88.9264899 7.8214 0 0 3 0
136 61.8396633 7.3929 1 1 3 0
137 30.6643266 7.1786 14 0 3 0
138 60.8175 8.6786 5 0 3 0
139 53.6625 6.8929 2 0 3 1
140 14.8210101 8.9286 0 1 3 0
141 54.6846633 7.8571 0 0 3 1
142 68.4835101 7.9643 0 1 3 1
143 64.9060101 7.8929 2 0 3 1
144 121.635 6.9643 1 1 3 1
145 28.62 2.9286 8 0 3 1
146 54.1735101 8.75 4 1 3 0
147 17.8875 7.75 3 0 3 1
148 58.7731734 7.5 3 1 3 1
149 101.7031734 4.25 25 0 3 1
150 42.4189899 8.5714 24 0 3 1
151 99.1478367 5.3571 1 1 3 0
152 113.9689899 5.5714 3 1 3 0
153 59.7953367 7.7857 1 0 3 1
154 48.0406734 7 3 1 3 1
155 96.5925 7.25 10 0 3 1
156 72.0610101 7.6429 1 1 3 1
157 60.8175 3.7857 6 1 3 1
158 47.0185101 4.6786 5 1 3 0
159 17.8875 2.9286 6 0 3 1
160 121.635 6.75 6 1 3 0
161 118.0575 6.7143 6 1 3 1
162 124.7014899 3.1786 4 0 3 1
163 63.8839899 7.6429 10 0 3 1
164 85.86 6.9286 3 0 3 1
165 119.5906734 7.2143 3 0 4 1
166 28.1089899 5.3571 4 1 4 1
167 36.7971633 6.9286 5 1 4 0
168 68.4835101 4 11 0 4 1
169 62.3506734 5.0357 0 0 4 1
170 42.93 6.8571 3 1 4 0
171 40.3746633 6.2857 5 0 4 0
172 12.7768266 6.6071 3 0 4 1
173 46.5075 7.3571 0 0 4 1
174 121.635 7.3929 6 0 4 1
175 94.0371633 6.4286 5 0 4 1
176 50.5960101 7.25 0 1 4 0
177 38.8414899 7.8929 5 1 4 0
178 93.5260101 6.4286 6 1 4 0
179 96.5925 7.2857 7 0 4 0
180 105.7918266 5.9643 5 0 4 1
181 96.0814899 7.2857 9 0 4 1
182 10.7325 6.4286 3 1 4 1
183 50.5960101 9.5357 5 0 4 0
184 131.8564899 6.7143 4 1 4 1
185 60.3064899 3.9286 2 1 4 0
186 70.5278367 5.5714 10 0 4 0
187 26.0646633 9.2143 8 0 4 0
188 73.0831734 8.7143 1 1 4 1
189 139.5225 10.6071 9 1 4 1
190 93.5260101 4.5714 2 0 4 0
191 139.5225 7.8929 3 1 5 1
192 33.7306734 7.5357 1 1 5 0
193 103.7475 9.1071 6 1 5 0
194 33.2196633 7.8929 8 1 5 0
195 83.3046633 9.5 2 0 5 1
196 128.79 7.8571 7 1 5 0
197 96.5925 6.5 14 0 5 1
198 96.5925 6.5714 10 0 5 0
199 88.9264899 6.6786 10 0 5 0
200 114.48 8.3214 12 0 5 0
201 111.4135101 6.4643 8 1 5 0
202 88.9264899 7.7857 8 0 5 0
203 62.8618266 8.2143 5 0 5 0
204 103.7475 6.6071 7 1 5 0
205 113.9689899 6.6429 9 1 5 1
206 139.5225 10.5714 10 1 5 1
207 22.9981734 7.4643 0 1 5 0
208 42.93 8.8929 38 1 5 1
209 96.5925 6 18 0 5 1
210 42.93 8.1429 11 0 5 0
211 90.9706734 7.25 20 0 5 1
212 105.2806734 8.3571 5 1 5 0
213 67.9725 6.8929 4 0 5 0
214 58.2621633 7.7143 13 0 5 1
215 20.9539899 9.1429 0 0 5 0
216 32.7085101 7.4286 4 0 5 1
217 139.5225 6.75 3 1 5 0
218 82.7935101 7.7143 0 1 5 0
219 25.5535101 9.5 1 1 5 0
220 53.1514899 8 1 1 5 0
221 82.7935101 8.75 1 0 5 0
222 67.9725 7.1071 4 0 5 0
223 57.7510101 7.4286 0 1 5 0
224 54.6846633 5.9286 1 1 5 1
225 61.8396633 7.0357 8 0 5 0
226 73.5943266 7.5714 4 0 5 0
227 10.7325 7.7857 4 1 5 0
228 37.8193266 7.0714 19 0 5 0
229 12.7768266 4 1 1 5 0
230 28.62 6.5357 2 0 5 0
231 85.86 7.6071 2 1 5 0
232 79.7271633 6.6429 7 0 5 0
233 103.7475 7.1429 5 0 5 0
234 39.3525 7.9643 10 1 5 0
235 96.0814899 7.5 3 1 5 1
236 39.3525 2.9286 3 0 5 0
237 96.5925 4 1 1 5 0
238 73.0831734 6.1071 5 1 5 0
239 45.9964899 7.1071 3 1 5 0
240 94.0371633 7.5 2 0 5 1
241 33.2196633 6.75 9 1 5 1
242 59.7953367 6.5714 0 1 5 0
243 113.9689899 5.5357 13 1 5 0
244 69.5056734 8.0357 22 1 5 0
245 54.6846633 7.1071 1 0 5 1
246 27.0868266 6.8571 8 0 5 0
247 10.7325 10.6071 3 1 5 1
248 32.1975 9.1786 3 0 5 0
249 96.5925 7.8571 5 1 5 1
250 96.0814899 6.7143 1 1 5 0
251 60.8175 7.9643 0 0 5 0
252 121.635 8.5357 3 1 5 0
253 67.9725 6.0714 3 0 5 0
254 121.635 6.25 4 1 5 1
255 50.085 8.6429 2 0 5 0
256 39.8635101 6.2857 5 0 5 0
257 71.55 8.4286 12 0 5 1
258 108.8581734 6.5 2 1 5 0
259 96.5925 7.1071 4 0 5 0
260 30.6643266 7.25 4 0 5 0
261 69.5056734 2.9286 2 1 5 1
262 56.7289899 7.8571 3 0 5 0
263 100.6810101 6.9643 1 1 5 0
264 103.7475 8.4643 9 1 5 1
265 95.5703367 5.9286 8 1 5 0
266 55.1956734 8.3214 9 0 5 1
267 96.5925 6.2857 0 0 5 1
268 88.9264899 7.2857 0 0 5 1
269 25.0425 7.25 7 1 5 0
270 89.9485101 7.7857 0 1 5 0
271 113.9689899 4.2143 16 0 5 1
272 53.1514899 6.6429 9 0 5 1
273 71.0389899 9.6071 0 1 5 1
274 39.3525 7.6786 5 1 5 1
275 8.1771633 8.0357 5 1 5 1
276 96.5925 6.3571 0 0 5 1
277 59.7953367 7.5 9 1 5 0
278 96.5925 5.9643 7 0 5 1
279 82.7935101 6.6429 10 1 5 0
280 64.9060101 7.3214 21 1 5 1
281 32.1975 8.3571 1 1 5 0
282 60.3064899 7.2143 3 0 5 1
283 96.0814899 5.7857 6 0 5 1
284 82.7935101 7.4643 9 1 5 0
285 53.6625 7.0714 13 1 5 0
286 54.6846633 8.7143 0 0 5 1
287 85.3489899 7.3929 2 1 5 0
288 106.3028367 4 26 1 5 1
289 92.5039899 6.1429 4 1 5 0
290 85.86 6.6786 9 0 5 1
291 121.1239899 5.9286 6 1 5 1
292 71.0389899 7.3214 2 0 5 0
293 64.9060101 8.6786 9 1 5 1
294 60.8175 8.7857 0 0 5 0
295 52.1293266 6.5 7 0 5 0
296 139.5225 7.6429 6 1 5 0
297 53.6625 5.0714 3 1 5 1
298 85.86 7.5357 2 0 5 0
299 35.2639899 6.7143 6 1 5 0
300 71.0389899 7.3929 3 0 5 0
301 35.775 7 4 0 5 0
302 83.3046633 6.2857 3 0 5 0
303 60.8175 5.75 29 1 5 1
304 93.5260101 6.3214 8 0 5 0
305 41.9078367 6.9286 0 1 5 0
306 60.8175 7.2143 3 1 5 1
307 71.0389899 7.5714 8 1 5 0
308 48.0406734 6.6429 2 0 5 0
309 65.9281734 7.9286 1 1 5 1
310 96.0814899 7.5357 9 0 5 0
311 63.8839899 7.4643 6 1 5 1
312 56.7289899 8.75 4 0 5 0
313 65.9281734 8.2143 0 0 5 0
314 60.8175 6.9286 4 0 5 0
315 65.9281734 3.6786 13 1 5 1
316 56.7289899 7.6429 1 0 5 0
317 81.2603367 10.6071 1 0 5 1
318 60.8175 6.3571 7 0 5 0
319 113.9689899 5.9286 7 0 5 1
320 108.8581734 6.75 7 1 5 1
321 22.9981734 5.8929 6 1 5 0
322 26.0646633 7.3571 5 0 5 0
323 41.3968266 8.5357 2 1 5 0
324 85.86 7.1071 3 1 5 0
325 60.8175 7.1429 1 0 5 1
326 139.5225 6.6071 3 1 5 0
327 124.1903367 2.9286 2 1 5 0
328 73.0831734 8.5 5 1 5 0
329 78.705 8.0357 10 0 5 1
330 101.1921633 7.6786 18 0 5 1
331 42.93 8.9643 3 0 5 0
332 68.4835101 8.0714 7 0 5 0
333 38.8414899 7 7 0 5 1
334 93.015 6.4643 5 0 5 0
335 10.7325 10.6071 1 1 5 0
336 45.9964899 6.7143 0 0 5 0
337 116.5243266 6.7857 5 1 5 0
338 103.7475 7.9643 9 0 5 1
339 45.4853367 7.7143 8 0 5 0
340 93.015 8.6429 1 1 5 0
341 60.3064899 7.5357 22 0 5 0
342 75.6385101 7.5 1 0 5 0
343 53.1514899 4.6429 14 0 5 1
344 50.085 8.7857 7 0 5 0
345 63.8839899 5.75 2 1 5 0
346 53.1514899 5.3571 8 1 5 1
347 14.8210101 7.4286 3 0 5 0
348 94.0371633 5.25 4 1 5 1
349 60.8175 9.25 2 1 5 0
350 28.62 8.4286 1 0 5 0
351 93.015 6.9643 2 1 5 0
352 29.1310101 9.0357 7 0 5 0
353 54.6846633 8 4 1 5 0
354 28.1089899 8.1071 0 0 5 0
355 78.705 8.8214 3 1 5 0
356 45.9964899 5.3214 5 0 5 0
357 76.1496633 7.6429 2 1 5 0
358 63.3728367 7.2857 3 1 5 0
359 30.1531734 7.0714 3 0 5 1
360 124.7014899 8.4643 7 0 5 0
361 96.0814899 5.4286 4 0 5 1
362 25.0425 6.7857 1 1 5 0
363 27.0868266 8.3929 1 1 5 0
364 40.8856734 7 1 1 5 0
365 67.9725 6.8571 6 0 5 0
366 35.2639899 8.8571 0 1 5 0
367 53.6625 8.5714 3 0 5 0
368 53.6625 8.2143 5 1 5 0
369 98.6368266 6.2857 2 1 5 0
370 90.9706734 7.1071 10 1 5 0
371 75.1275 5.6429 1 0 5 1
372 52.6403367 8.5357 5 0 5 1
373 75.1275 7.5714 0 1 5 0
374 28.1089899 8.1071 3 0 5 0
375 75.1275 7.5 5 1 5 0
376 27.0868266 8.6786 12 0 5 1
377 51.1071633 6.9286 3 1 5 1
378 96.5925 9.0357 12 0 5 0
379 82.2825 7.75 11 1 5 1
380 71.55 8.25 30 0 5 1
381 40.3746633 9 0 1 5 0
382 67.9725 5.4286 2 1 5 0
383 39.3525 5.7143 5 0 5 0
384 82.7935101 7.8214 8 1 5 0
385 96.0814899 7.1429 2 1 5 0
386 121.1239899 6.9286 19 1 5 1
387 81.7714899 9.2857 16 0 5 1
388 83.3046633 4.5714 2 1 5 0
389 78.1939899 5.3571 6 0 5 1
390 85.3489899 7.2857 4 0 5 0
391 42.93 8 7 0 5 1
392 45.9964899 9.1429 0 0 5 1
393 114.48 6.3571 1 0 5 0
394 65.4171633 7.6429 6 0 5 1
395 96.5925 6.4286 2 1 5 0
396 58.2621633 6.9286 3 0 5 0
397 73.5943266 7.6071 2 1 5 1
398 53.6625 5.5357 4 0 5 0
399 60.8175 7.7143 19 0 5 0
400 114.9910101 7.0357 15 1 5 1
401 74.6164899 8 1 0 5 1
402 114.9910101 4.1786 2 1 5 1
403 63.3728367 6.6786 10 1 5 1
404 70.0168266 8.1429 12 1 5 0
405 73.5943266 6.3571 1 0 5 0
406 37.3081734 7.4643 12 1 5 1
407 65.4171633 5.4643 2 1 5 0
408 50.085 7.3929 0 1 5 0
409 27.0868266 6.6786 0 1 5 0
410 63.8839899 7.6786 12 1 5 1
411 20.9539899 8.3571 6 1 5 0
412 33.7306734 5.8571 0 1 5 0
413 52.1293266 8.7143 1 0 5 1
414 12.7768266 7.8571 2 0 5 1
415 26.0646633 8.6071 4 1 5 1
416 78.1939899 9.1786 2 1 5 0
417 81.2603367 6.1429 5 0 5 0
418 60.8175 7.2857 1 1 5 0
419 85.86 8.9286 4 0 5 0
420 48.0406734 7.4286 4 0 5 0
421 45.9964899 9.0714 5 0 5 1
422 39.8635101 7.2143 8 0 5 1
423 67.4614899 7.8571 3 0 5 0
424 96.0814899 7 5 1 5 0
425 93.5260101 8.2857 7 1 5 0
426 84.8378367 7.8571 2 0 5 0
427 85.3489899 5.5 9 0 5 0
428 106.8139899 6.5714 15 0 5 0
429 78.705 7.7143 3 0 5 0
430 82.2825 6.6786 2 1 5 0
431 55.7068266 8.8571 1 1 5 1
432 47.5296633 8.0714 1 1 5 1
433 81.2603367 8.1429 6 1 5 1
434 60.8175 6.7857 6 0 5 1
435 12.7768266 8.6429 5 1 5 1
436 75.1275 6.5 1 1 5 0
437 44.4631734 5.9643 7 1 5 0
438 76.6606734 4.5714 2 0 5 0
439 60.8175 7.2857 4 1 5 0
440 81.7714899 8.1786 1 0 5 0
441 88.9264899 5.4286 6 0 5 1
442 96.5925 7.0714 10 0 5 1
443 82.7935101 3.8214 5 1 5 0
444 111.4135101 6.1429 5 0 5 0
;
run;
Here are the the distribution, mean, and variance for Errors:
| 55 |
12.39 |
55 |
12.39 |
| 60 |
13.51 |
115 |
25.90 |
| 57 |
12.84 |
172 |
38.74 |
| 53 |
11.94 |
225 |
50.68 |
| 35 |
7.88 |
260 |
58.56 |
| 37 |
8.33 |
297 |
66.89 |
| 25 |
5.63 |
322 |
72.52 |
| 27 |
6.08 |
349 |
78.60 |
| 19 |
4.28 |
368 |
82.88 |
| 17 |
3.83 |
385 |
86.71 |
| 15 |
3.38 |
400 |
90.09 |
| 3 |
0.68 |
403 |
90.77 |
| 8 |
1.80 |
411 |
92.57 |
| 6 |
1.35 |
417 |
93.92 |
| 4 |
0.90 |
421 |
94.82 |
| 2 |
0.45 |
423 |
95.27 |
| 3 |
0.68 |
426 |
95.95 |
| 1 |
0.23 |
427 |
96.17 |
| 2 |
0.45 |
429 |
96.62 |
| 3 |
0.68 |
432 |
97.30 |
| 1 |
0.23 |
433 |
97.52 |
| 1 |
0.23 |
434 |
97.75 |
| 2 |
0.45 |
436 |
98.20 |
| 2 |
0.45 |
438 |
98.65 |
| 1 |
0.23 |
439 |
98.87 |
| 1 |
0.23 |
440 |
99.10 |
| 1 |
0.23 |
441 |
99.32 |
| 1 |
0.23 |
442 |
99.55 |
| 1 |
0.23 |
443 |
99.77 |
| 1 |
0.23 |
444 |
100.00 |
My instinct was to use a model with a Poisson distribution; however, I realize I need a different distribution due to the overdispersion of Errors. Here was my Poisson model:
proc genmod data=forSAS plots=none namelen=65;
class Female Location Income_thresh;
model Errors=LPA_Daily_min ST_win Female Location Income_thresh /
dist=Poisson;run;
I do not know whether to instead use zero-inflated Poisson, negative binomial, or a zero-inflated negative binomial distribution. Does anyone know how I can determine which distribution is most suitable, and how to justify that (e.g., in a manuscript for publication), like a citation, significance test, and/or threshold number of a certain statistic? Thank you.
