# How to use quasi-Poisson model after overdisperson with glmer(mydata,family = poisson(link = 'log'))?

I have to fit my data with Laplace glmm with random effect using poisson distribution error.

m1 =  glmer(y ~  x +  SIDI +  z.fac +
(1|SITE) + (1|DATE), family = poisson(link = 'log'), data=dat)


But when I use an overdispersion.test, it indicates overdispersion with p-value < 0.05

And then, a paper told me I should proceed quasi-possion refit, however:

    m1b =  glmer(y~  x +  SIDI +  z.fac +
(1|SITE) + (1|DATE), family = quasipoisson(link = 'log'), data=dat)


It told me that quasi+ distribution shouldn't be applying glmer(). And I know I can use it in glm(family), but my data needs to consider random effect. Who can tell me what should I do when proceeding quasipoisson refit model (don't forget the random effects). By the way , glmer( offset(log(x)) ) and glmer( log(x) ), between them, have any difference? what's the offset() meaning? I can't comprehend what the document tells with help(offset).

 temp <- structure(list(DATE=structure(c(17684,17684,17684,17684,
17684,17684,17684,17684,17684,17684,17684,17684,17684,
17684,17684,17686,17686,17686,17686,17686,17686,17686,
17686,17686,17686,17686,17686,17687,17687,17687,17687,
17687,17687,17687,17687,17687,17688,17688,17688,17688,
17688,17688,17688,17688,17688,17688,17688,17688,17689,
17689,17689,17689,17689,17689,17689,17689,17689,17689,
17689,17689,17690,17690,17690,17690,17690,17690,17690,
17690,17690,17690,17690,17690,17690,17690,17690,17691,
17691,17691,17691,17691,17691,17691,17691,17691,17691,
17691,17691,17692,17692,17692,17692,17692,17692,17692,
17692,17692,17693,17693,17693,17693,17693,17693,17693,
17693,17693,17693,17693,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17694,17694,17694,17694,17694,17694,17694,17694,
17694,17695,17695,17695,17695,17695,17695,17695,17695,
17695,17695,17695,17695,17695,17695,17695,17696,17696,
17696,17696,17696,17696,17696,17696,17696,17696,17696,
17696,17697,17697,17697,17697,17697,17697,17697,17697,
17697,17697,17697,17697,17697,17698,17698,17698,17698,
17698,17698,17699,17699,17699,17699,17699,17699,17699,
17699,17699,17702,17702,17702,17702,17702,17702,17702,
17702,17702,17702,17702,17702,17702,17702,17702,17703,
17703,17703,17703,17703,17703,17703,17703,17703,17703,
17703,17703,17704,17704,17704,17704,17704,17704,17704,
17704,17704,17705,17705,17705,17705,17705,17705,17705,
17705,17705,17705,17705,17705,17706,17706,17706,17706,
17706,17706,17706,17706,17706,17706,17706,17706,17709,
17709,17709,17709,17709,17709,17709,17709,17709,17709,
17709,17709,17710,17710,17710,17710,17710,17710,17710,
17710,17710,17710,17711,17711,17711,17711,17711,17711,
17711,17712,17712,17712,17712,17712,17712,17712,17712,
17712,17712,17713,17713,17713,17713,17713,17713,17713,
17713,17713,17713,17713,17713,18053,18053,18053,18053,
18053,18053,18053,18053,18053,18053,18053,18053,18053,
18053,18053,18053,18053,18053,18053,18059,18059,18059,
18059,18059,18059,18060,18060,18060,18060,18060,18060,
18061,18061,18061,18061,18061,18061,18061,18061,18061,
18061,18061,18061,18061,18061,18061,18061,18061,18061,
18066,18066,18066,18066,18066,18066,18066,18066,18066,
18066,18066,18066,18066,18067,18067,18067,18067,18067,
18067,18067,18067,18067,18067,18067,18067,18067,18067,
18067,18067,18067,18067,18067,18067,18067,18067,18068,
18068,18068,18068,18068,18068,18068,18068,18068,18073,
18073,18073,18073,18073,18073,18073,18073,18073,18073,
18073,18073,18073,18073,18073,18073,18074,18074,18074,
18074,18074,18074,18074,18074,18074,18074,18074,18074,
18074,18074,18074,18074,18074,18074,18075,18075,18075,
18075,18075,18075,18075,18075,18075,18075,18075,18075,
18075,18075,18075,18075,18075,18075),class="Date"),SITE=structure(c(1L,
1L,1L,2L,2L,2L,3L,3L,3L,4L,4L,4L,5L,5L,5L,6L,6L,
6L,7L,7L,7L,8L,8L,8L,9L,9L,9L,10L,10L,10L,11L,11L,
11L,12L,12L,12L,13L,13L,13L,14L,14L,14L,15L,15L,15L,
16L,16L,16L,17L,17L,17L,18L,18L,18L,19L,19L,19L,20L,
20L,20L,1L,1L,1L,2L,2L,2L,3L,3L,3L,4L,4L,4L,5L,
5L,5L,6L,6L,6L,7L,7L,7L,8L,8L,8L,9L,9L,9L,10L,
10L,10L,11L,11L,11L,12L,12L,12L,13L,13L,13L,14L,14L,
14L,15L,15L,16L,16L,16L,17L,17L,17L,17L,17L,17L,17L,
17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,
17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,
17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,
17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,
17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,17L,
17L,17L,17L,17L,17L,17L,18L,18L,18L,19L,19L,19L,20L,
20L,20L,1L,1L,1L,2L,2L,2L,3L,3L,3L,4L,4L,4L,5L,
5L,5L,6L,6L,6L,7L,7L,7L,8L,8L,8L,9L,9L,9L,10L,
10L,10L,11L,11L,11L,12L,14L,14L,14L,15L,15L,15L,13L,
13L,13L,16L,16L,16L,18L,18L,18L,19L,19L,19L,20L,20L,
20L,1L,1L,1L,2L,2L,2L,3L,3L,3L,4L,4L,4L,5L,5L,
5L,6L,6L,6L,7L,7L,7L,8L,8L,8L,9L,9L,9L,10L,10L,
10L,11L,11L,11L,12L,12L,12L,13L,13L,13L,14L,14L,14L,
15L,15L,15L,16L,16L,16L,17L,17L,17L,18L,18L,18L,19L,
19L,19L,20L,20L,20L,1L,1L,1L,2L,2L,2L,3L,3L,3L,
4L,5L,5L,6L,6L,6L,7L,8L,8L,8L,9L,9L,9L,10L,11L,
11L,11L,12L,12L,12L,13L,13L,13L,14L,15L,15L,15L,16L,
16L,16L,17L,17L,17L,18L,18L,18L,19L,19L,19L,20L,20L,
20L,21L,22L,23L,24L,25L,26L,27L,28L,29L,30L,31L,31L,
32L,33L,34L,35L,36L,37L,38L,21L,31L,32L,33L,34L,35L,
22L,23L,24L,36L,37L,38L,25L,25L,25L,26L,26L,26L,27L,
27L,27L,28L,28L,28L,29L,29L,29L,30L,30L,30L,21L,21L,
21L,31L,33L,33L,33L,34L,34L,34L,35L,35L,35L,22L,22L,
22L,23L,23L,23L,24L,24L,24L,29L,29L,29L,32L,36L,36L,
36L,37L,37L,37L,38L,38L,38L,25L,26L,27L,27L,27L,28L,
30L,30L,30L,21L,21L,21L,31L,31L,31L,32L,32L,32L,33L,
33L,33L,34L,35L,35L,35L,22L,22L,22L,23L,23L,23L,24L,
24L,24L,36L,36L,36L,37L,37L,37L,38L,38L,38L,25L,25L,
25L,26L,26L,26L,27L,27L,27L,28L,28L,28L,29L,29L,29L,
30L,30L,30L),.Label=c("CB1","CB2","CB3","CB4","CB5",
"CB6","CB7","CB8","CB9","CB10","CB11","CB12","CB13","CB14",
"CB15","CB16","CB17","CB18","CB19","CB20","CC1","CC10",
"CC11","CC12","CC13","CC14","CC15","CC16","CC17","CC18",
"CC2","CC3","CC4","CC5","CC6","CC7","CC8","CC9","cc1",
"cc10","cc11","cc12","cc13","cc14","cc15","cc16","cc17",
"cc18","cc2","cc3","cc4","cc5","cc6","cc7","cc8","cc9"
),class="factor"),y=c(0L,0L,8L,0L,16L,20L,0L,8L,
4L,4L,0L,4L,0L,0L,0L,24L,0L,24L,0L,4L,0L,0L,0L,
8L,0L,24L,4L,0L,4L,0L,4L,0L,0L,0L,88L,4L,0L,12L,
0L,4L,0L,0L,0L,0L,0L,8L,0L,12L,0L,0L,0L,0L,0L,
4L,0L,0L,0L,12L,12L,12L,0L,16L,32L,48L,16L,36L,0L,
0L,4L,0L,48L,0L,0L,0L,0L,0L,0L,8L,8L,12L,16L,16L,
8L,0L,52L,56L,36L,4L,4L,8L,0L,0L,0L,4L,12L,4L,16L,
4L,8L,4L,0L,0L,0L,0L,8L,8L,24L,0L,0L,0L,0L,0L,
0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,4L,0L,0L,
0L,0L,0L,0L,0L,0L,0L,0L,0L,4L,0L,0L,0L,0L,0L,0L,
0L,0L,0L,0L,0L,0L,0L,0L,4L,0L,4L,0L,0L,0L,4L,4L,
0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,
0L,0L,0L,0L,0L,0L,20L,32L,4L,24L,0L,0L,0L,0L,0L,
8L,8L,32L,20L,52L,36L,72L,52L,52L,12L,4L,16L,0L,
0L,4L,4L,0L,0L,20L,8L,0L,16L,32L,32L,0L,12L,20L,
24L,8L,40L,92L,20L,28L,8L,32L,92L,0L,4L,4L,0L,8L,
20L,4L,20L,4L,12L,28L,24L,8L,16L,36L,84L,8L,0L,0L,
16L,44L,48L,4L,0L,0L,20L,24L,12L,40L,136L,188L,0L,
24L,44L,12L,32L,40L,0L,8L,32L,24L,16L,8L,12L,16L,
12L,12L,12L,24L,16L,80L,68L,20L,12L,44L,28L,36L,12L,
56L,168L,48L,20L,40L,64L,4L,0L,0L,20L,4L,28L,8L,
4L,12L,76L,60L,48L,12L,4L,0L,4L,20L,28L,4L,4L,8L,
20L,56L,28L,392L,328L,476L,60L,4L,0L,116L,72L,84L,
8L,260L,284L,140L,60L,184L,4L,124L,108L,48L,48L,288L,
608L,528L,148L,136L,40L,0L,84L,120L,16L,92L,116L,76L,
32L,8L,4L,28L,28L,24L,0L,12L,4L,40L,20L,92L,0L,0L,
0L,0L,8L,0L,40L,0L,0L,0L,0L,0L,0L,0L,0L,0L,0L,
0L,0L,0L,4L,12L,8L,0L,0L,0L,0L,4L,0L,0L,0L,0L,
0L,0L,0L,0L,0L,0L,0L,0L,4L,0L,0L,4L,16L,32L,0L,
0L,4L,4L,60L,116L,4L,0L,12L,0L,0L,0L,0L,0L,0L,0L,
0L,0L,0L,28L,0L,20L,0L,0L,0L,88L,24L,12L,16L,0L,
0L,0L,0L,0L,0L,0L,0L,8L,16L,0L,8L,0L,0L,0L,20L,
28L,24L,68L,168L,64L,0L,0L,0L,304L,4L,24L,4L,0L,
4L,0L,0L,0L,0L,0L,4L,0L,4L,4L,4L,0L,0L,0L,0L,0L,
4L,0L,8L,4L,4L,0L,0L,32L,68L,28L,0L,0L,0L,80L,0L,
4L,12L,4L,8L,12L,48L,0L,24L,40L,88L),x=c(13168L,
2168L,1240L,1916L,3876L,15732L,1056L,1984L,1548L,1184L,
1676L,2212L,288L,556L,416L,14800L,4436L,6360L,808L,1348L,
3216L,988L,1180L,948L,10152L,32172L,5356L,1704L,5612L,
2636L,10012L,3980L,6116L,3340L,2684L,1088L,2796L,7768L,
2428L,464L,712L,496L,4568L,5084L,5400L,464L,1088L,1260L,
316L,292L,336L,4724L,11180L,8760L,2936L,2056L,3412L,
3724L,3204L,2120L,51932L,65564L,93480L,69792L,67688L,
89692L,9932L,22492L,13888L,1084L,804L,412L,11568L,16632L,
10724L,21704L,19960L,40636L,17056L,18184L,6184L,2704L,
1932L,2576L,19456L,41404L,34416L,10000L,16336L,8856L,
60480L,55052L,117396L,31004L,33620L,27588L,4944L,14288L,
2784L,816L,456L,764L,1056L,3260L,19876L,12084L,9128L,
288L,132L,432L,300L,144L,108L,172L,196L,36L,20L,88L,
132L,144L,84L,520L,76L,1000L,204L,440L,104L,260L,160L,
520L,80L,180L,132L,204L,96L,28L,52L,560L,120L,16L,
16L,64L,120L,208L,28L,36L,40L,12L,44L,240L,20L,52L,
28L,0L,220L,12L,160L,280L,276L,1880L,28L,44L,376L,
580L,48L,128L,160L,72L,28L,168L,60L,40L,92L,84L,148L,
24L,20L,244L,280L,72L,92L,56L,6788L,5672L,1448L,72860L,
106248L,70972L,79452L,92504L,98108L,37696L,41480L,50116L,
275372L,403224L,451172L,368936L,394448L,303560L,42784L,
141940L,289936L,3440L,4828L,7984L,7508L,4356L,3800L,100580L,
156052L,121284L,161308L,108888L,80868L,9576L,7980L,11876L,
31592L,54008L,88916L,27844L,20844L,25264L,394000L,336804L,
530008L,3748L,6004L,5324L,6244L,26700L,24696L,11984L,
11876L,12512L,10500L,4332L,3632L,4552L,584852L,862216L,
796300L,2116L,2076L,1880L,473620L,468804L,418832L,4496L,
2584L,2024L,6836L,7432L,10356L,1144660L,897788L,1015528L,
61676L,49192L,83880L,23600L,49756L,45180L,252220L,490040L,
410024L,116888L,216488L,146652L,13424L,22936L,20376L,5152L,
3588L,2956L,261124L,316888L,303800L,35748L,19868L,17056L,
136712L,213704L,277568L,392644L,527116L,593788L,191296L,
244312L,233852L,2448L,2300L,2492L,41044L,91080L,156684L,
4468L,5536L,10992L,526120L,466640L,145332L,14484L,18680L,
21520L,11172L,83512L,84088L,29496L,45056L,26240L,22276L,
59052L,56116L,425020L,585604L,599200L,931520L,78796L,8508L,
43156L,24560L,100284L,2912L,609400L,677832L,592504L,98044L,
118460L,106804L,678400L,49360L,45700L,40500L,1365272L,
1234296L,1188048L,20840L,23380L,11580L,476L,41380L,19712L,
10312L,81124L,123560L,168060L,36920L,43000L,37884L,3856L,
10064L,32160L,4288L,6136L,3852L,72020L,167572L,342444L,
3536L,328L,160L,4L,2180L,1056L,2536L,1232L,6544L,600L,
2248L,4868L,6252L,584L,1468L,368L,132L,260L,140L,31236L,
43184L,90728L,4740L,5380L,5984L,2300L,1464L,1088L,900L,
48L,1608L,10280L,11108L,15444L,20040L,17288L,39596L,14072L,
33632L,56580L,9964L,23600L,7628L,45324L,45132L,34376L,
2140L,2524L,1632L,734660L,900288L,983124L,298628L,3212L,
3080L,3116L,23888L,43948L,85296L,31360L,19836L,19956L,
13544L,9940L,10048L,11332L,6896L,10888L,1036L,796L,896L,
412016L,437348L,555224L,76120L,10312L,20948L,12024L,2984L,
2576L,2852L,4244L,3740L,380L,325440L,40L,17744L,26260L,
23444L,164L,8396L,19780L,22664L,548164L,514468L,340464L,
912L,276L,152L,7244L,5348L,6928L,47208L,62488L,34304L,
3632L,4136L,3568L,4748L,32484L,35860L,41480L,204176L,
331408L,273684L,35184L,18840L,16948L,25580L,31940L,24160L,
20700L,18496L,19928L,32280L,21800L,28688L,806488L,854176L,
1259328L,29204L,25984L,22440L,85680L,76400L,99120L,37052L,
38172L,48892L,46584L,65264L,71680L,256260L,370332L,363968L
),z.fac=structure(c(2L,2L,2L,2L,2L,2L,1L,1L,1L,3L,
3L,3L,4L,4L,4L,2L,2L,2L,4L,4L,4L,2L,2L,2L,1L,1L,
1L,4L,4L,4L,3L,3L,3L,2L,2L,2L,3L,3L,3L,3L,3L,3L,
2L,2L,2L,2L,2L,2L,3L,3L,3L,2L,2L,2L,4L,4L,4L,2L,
2L,2L,2L,2L,2L,2L,2L,2L,1L,1L,1L,3L,3L,3L,4L,4L,
4L,2L,2L,2L,4L,4L,4L,2L,2L,2L,1L,1L,1L,4L,4L,4L,
3L,3L,3L,2L,2L,2L,3L,3L,3L,3L,3L,3L,2L,2L,2L,2L,
2L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,
3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,
3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,
3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,
3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,3L,2L,
2L,2L,4L,4L,4L,2L,2L,2L,2L,2L,2L,2L,2L,2L,1L,1L,
1L,3L,3L,3L,4L,4L,4L,2L,2L,2L,4L,4L,4L,2L,2L,2L,
1L,1L,1L,4L,4L,4L,3L,3L,3L,2L,3L,3L,3L,2L,2L,2L,
3L,3L,3L,2L,2L,2L,2L,2L,2L,4L,4L,4L,2L,2L,2L,2L,
2L,2L,2L,2L,2L,1L,1L,1L,3L,3L,3L,4L,4L,4L,2L,2L,
2L,4L,4L,4L,2L,2L,2L,1L,1L,1L,4L,4L,4L,3L,3L,3L,
2L,2L,2L,3L,3L,3L,3L,3L,3L,2L,2L,2L,2L,2L,2L,3L,
3L,3L,2L,2L,2L,4L,4L,4L,2L,2L,2L,2L,2L,2L,2L,2L,
2L,1L,1L,1L,3L,4L,4L,2L,2L,2L,4L,2L,2L,2L,1L,1L,
1L,4L,3L,3L,3L,2L,2L,2L,3L,3L,3L,3L,2L,2L,2L,2L,
2L,2L,3L,3L,3L,2L,2L,2L,4L,4L,4L,2L,2L,2L,2L,3L,
3L,4L,1L,3L,3L,3L,2L,2L,1L,1L,4L,3L,5L,3L,2L,2L,
2L,2L,1L,4L,3L,5L,3L,3L,3L,4L,2L,2L,2L,1L,1L,1L,
3L,3L,3L,3L,3L,3L,3L,3L,3L,2L,2L,2L,2L,2L,2L,2L,
2L,2L,1L,3L,3L,3L,5L,5L,5L,3L,3L,3L,3L,3L,3L,3L,
3L,3L,4L,4L,4L,2L,2L,2L,4L,2L,2L,2L,2L,2L,2L,2L,
2L,2L,1L,3L,3L,3L,3L,3L,2L,2L,2L,2L,2L,2L,1L,1L,
1L,4L,4L,4L,3L,3L,3L,5L,3L,3L,3L,3L,3L,3L,3L,3L,
3L,4L,4L,4L,2L,2L,2L,2L,2L,2L,2L,2L,2L,1L,1L,1L,
3L,3L,3L,3L,3L,3L,3L,3L,3L,2L,2L,2L,2L,2L,2L),.Label=c("0",
"1","2","3","4"),class="factor"),SIDI=c(0.6549,0.6549,
0.6549,0.819,0.819,0.819,0.7304,0.7304,0.7304,0.744,0.744,
0.744,0.7066,0.7066,0.7066,0.6495,0.6495,0.6495,0.8357,
0.8357,0.8357,0.4408,0.4408,0.4408,0.7161,0.7161,0.7161,
0.5601,0.5601,0.5601,0.5488,0.5488,0.5488,0.7409,0.7409,
0.7409,0.7505,0.7505,0.7505,0.4861,0.4861,0.4861,0.8634,
0.8634,0.8634,0.5299,0.5299,0.5299,0.8452,0.8452,0.8452,
0.7962,0.7962,0.7962,0.7968,0.7968,0.7968,0.8719,0.8719,
0.8719,0.6549,0.6549,0.6549,0.819,0.819,0.819,0.7304,
0.7304,0.7304,0.744,0.744,0.744,0.7066,0.7066,0.7066,
0.6495,0.6495,0.6495,0.8357,0.8357,0.8357,0.4408,0.4408,
0.4408,0.7161,0.7161,0.7161,0.5601,0.5601,0.5601,0.5488,
0.5488,0.5488,0.7409,0.7409,0.7409,0.7505,0.7505,0.7505,
0.4861,0.4861,0.4861,0.8634,0.8634,0.5299,0.5299,0.5299,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,
0.8452,0.8452,0.8452,0.8452,0.8452,0.8452,0.7962,0.7962,
0.7962,0.7968,0.7968,0.7968,0.8719,0.8719,0.8719,0.6549,
0.6549,0.6549,0.819,0.819,0.819,0.7304,0.7304,0.7304,
0.744,0.744,0.744,0.7066,0.7066,0.7066,0.6495,0.6495,
0.6495,0.8357,0.8357,0.8357,0.4408,0.4408,0.4408,0.7161,
0.7161,0.7161,0.5601,0.5601,0.5601,0.5488,0.5488,0.5488,
0.7409,0.4861,0.4861,0.4861,0.8634,0.8634,0.8634,0.7505,
0.7505,0.7505,0.5299,0.5299,0.5299,0.7962,0.7962,0.7962,
0.7968,0.7968,0.7968,0.8719,0.8719,0.8719,0.6549,0.6549,
0.6549,0.819,0.819,0.819,0.7304,0.7304,0.7304,0.744,0.744,
0.744,0.7066,0.7066,0.7066,0.6495,0.6495,0.6495,0.8357,
0.8357,0.8357,0.4408,0.4408,0.4408,0.7161,0.7161,0.7161,
0.5601,0.5601,0.5601,0.5488,0.5488,0.5488,0.7409,0.7409,
0.7409,0.7505,0.7505,0.7505,0.4861,0.4861,0.4861,0.8634,
0.8634,0.8634,0.5299,0.5299,0.5299,0.8452,0.8452,0.8452,
0.7962,0.7962,0.7962,0.7968,0.7968,0.7968,0.8719,0.8719,
0.8719,0.6549,0.6549,0.6549,0.819,0.819,0.819,0.7304,
0.7304,0.7304,0.744,0.7066,0.7066,0.6495,0.6495,0.6495,
0.8357,0.4408,0.4408,0.4408,0.7161,0.7161,0.7161,0.5601,
0.5488,0.5488,0.5488,0.7409,0.7409,0.7409,0.7505,0.7505,
0.7505,0.4861,0.8634,0.8634,0.8634,0.5299,0.5299,0.5299,
0.8452,0.8452,0.8452,0.7962,0.7962,0.7962,0.7968,0.7968,
0.7968,0.8719,0.8719,0.8719,0.7289,0.7263,0.6633,0.3309,
0.7317,0.7003,0.7932,0.8188,0.7889,0.7731,0.7882,0.7882,
0.8556,0.8002,0.8337,0.8385,0.7121,0.6724,0.3816,0.7289,
0.7882,0.8556,0.8002,0.8337,0.8385,0.7263,0.6633,0.3309,
0.7121,0.6724,0.3816,0.7317,0.7317,0.7317,0.7003,0.7003,
0.7003,0.7932,0.7932,0.7932,0.8188,0.8188,0.8188,0.7889,
0.7889,0.7889,0.7731,0.7731,0.7731,0.7289,0.7289,0.7289,
0.7882,0.8002,0.8002,0.8002,0.8337,0.8337,0.8337,0.8385,
0.8385,0.8385,0.7263,0.7263,0.7263,0.6633,0.6633,0.6633,
0.3309,0.3309,0.3309,0.7889,0.7889,0.7889,0.8556,0.7121,
0.7121,0.7121,0.6724,0.6724,0.6724,0.3816,0.3816,0.3816,
0.7317,0.7003,0.7932,0.7932,0.7932,0.8188,0.7731,0.7731,
0.7731,0.7289,0.7289,0.7289,0.7882,0.7882,0.7882,0.8556,
0.8556,0.8556,0.8002,0.8002,0.8002,0.8337,0.8385,0.8385,
0.8385,0.7263,0.7263,0.7263,0.6633,0.6633,0.6633,0.3309,
0.3309,0.3309,0.7121,0.7121,0.7121,0.6724,0.6724,0.6724,
0.3816,0.3816,0.3816,0.7317,0.7317,0.7317,0.7003,0.7003,
0.7003,0.7932,0.7932,0.7932,0.8188,0.8188,0.8188,0.7889,
0.7889,0.7889,0.7731,0.7731,0.7731)),row.names=c(NA,-505L
),class=c("data.table","data.frame"))

• Have a look here bbolker.github.io/mixedmodels-misc/glmmFAQ.html#overdispersion There you can find that the glmmTMB package provides support for a “quasi-Poisson” parameterization. Mar 8, 2020 at 4:48
• thank you very much . I will look it . Mar 8, 2020 at 4:52
• but I still have a question. First I used the lme4::glmer() with poisson family. If I turn to glmmTAB. Shall I give up the lme4::glmer. I mean that in all proceeds I only use glmmTMB to fit with Poisson and if overdisperson, I refit model with glmmTAB's quasi-Possion? Mar 8, 2020 at 5:28
• Can you tell ue which overdispersion test you used, and show its output? And, for your offset Q: stats.stackexchange.com/questions/100772/… Mar 8, 2020 at 12:29
• For overdispersion, instead of going "quasi", I'd try observation-level random effects (stats.stackexchange.com/questions/351352/…), i.e. add +(1|ID), where ID is just a unique character for each row in your data. Mar 8, 2020 at 14:44