GLIMMIX for count data in staggered-start design

[Lesley6145]

Hi, I'm new to this forum, but have used SAS for a number of years, and I am seeking guidance on proc GLIMMX.

I'm testing how well plants establish after herbicide treatment (herb) and seeding methods (seed) applied across a disturbed landscape (fixed effects). The design is a staggered start experiment so that time-since-treatment effect (fixed factor) can be separated from year effects (random factor) as follows:
-- Herbicide (2 levels) x seeding (3 levels) treatment combinations were randomly assigned to 24 plots (4 replicates per treatment combination) in each of 10 sites (blocking factor)
--The plots were treated with herbicide and seeding treatments across 3 successive years (i.e., plots were treated at 4 sites in 2018, at another 3 sites in 2019, and another 3 in 2020).
-- Seedlings were enumerated on plots (counts) for 2 years after treatments were implemented (e.g., plots treated in 2018 were measured in 2019 and 2020; plots treated in 2019 measured in 2020 and 2021, and so on for 2020 plots)
--There is also a covariate (Covar) that is a count of neighbor shrubs, measured on each plot in each year. It will be relevant for my second question.

I am using GLIMMIX to analyze herbicide, seeding, and time-since-treated and their interactions. I’m trying to estimate variances for the random effects, and as I am more familiar with MIXED, I’m unsure if I have the code written properly.

data exper1;
input Time	Year	Site	Herb$ Veg$ Plot Count Covar;
datalines;
2	2018	1	no	A	21	3	3
2	2018	1	no	A	25	12	5
2	2018	1	no	A	29	2	0
2	2018	1	no	A	32	1	1
2	2018	1	no	B	19	2	2
2	2018	1	no	B	22	10	13
2	2018	1	no	B	23	6	1
2	2018	1	no	B	30	6	7
2	2018	1	no	C	24	4	7
2	2018	1	no	C	26	4	4
2	2018	1	no	C	28	6	3
2	2018	1	no	C	31	3	3
2	2018	1	yes	A	5	0	5
2	2018	1	yes	A	6	7	3
2	2018	1	yes	A	7	3	1
2	2018	1	yes	A	10	1	4
2	2018	1	yes	B	3	6	3
2	2018	1	yes	B	4	2	6
2	2018	1	yes	B	12	1	3
2	2018	1	yes	B	16	1	5
2	2018	1	yes	C	2	5	7
2	2018	1	yes	C	9	5	6
2	2018	1	yes	C	14	9	10
2	2018	1	yes	C	15	14	6
2	2020	2	no	A	20	0	33
2	2020	2	no	A	21	0	34
2	2020	2	no	A	29	0	16
2	2020	2	no	A	32	0	47
2	2020	2	no	B	23	0	24
2	2020	2	no	B	24	0	31
2	2020	2	no	B	28	0	28
2	2020	2	no	B	31	0	37
2	2020	2	no	C	17	0	25
2	2020	2	no	C	18	1	20
2	2020	2	no	C	22	0	24
2	2020	2	no	C	26	0	28
2	2020	2	yes	A	10	0	24
2	2020	2	yes	A	12	0	24
2	2020	2	yes	A	13	0	8
2	2020	2	yes	A	15	0	5
2	2020	2	yes	B	3	3	35
2	2020	2	yes	B	6	0	25
2	2020	2	yes	B	9	0	44
2	2020	2	yes	B	14	0	40
2	2020	2	yes	C	2	0	50
2	2020	2	yes	C	8	0	26
2	2020	2	yes	C	11	0	14
2	2020	2	yes	C	16	0	5
2	2018	3	no	A	17	1	2
2	2018	3	no	A	24	1	0
2	2018	3	no	A	25	5	4
2	2018	3	no	A	32	3	3
2	2018	3	no	B	18	2	5
2	2018	3	no	B	29	1	0
2	2018	3	no	B	30	0	5
2	2018	3	no	B	31	0	0
2	2018	3	no	C	20	1	6
2	2018	3	no	C	23	0	3
2	2018	3	no	C	27	0	0
2	2018	3	no	C	28	0	0
2	2018	3	yes	A	4	2	5
2	2018	3	yes	A	14	1	0
2	2018	3	yes	A	15	2	2
2	2018	3	yes	A	16	0	0
2	2018	3	yes	B	5	0	1
2	2018	3	yes	B	9	0	0
2	2018	3	yes	B	12	1	1
2	2018	3	yes	B	13	0	0
2	2018	3	yes	C	1	9	5
2	2018	3	yes	C	7	2	0
2	2018	3	yes	C	8	0	0
2	2018	3	yes	C	10	1	3
2	2018	4	no	A	17	1	21
2	2018	4	no	A	20	5	24
2	2018	4	no	A	26	0	22
2	2018	4	no	A	27	4	27
2	2018	4	no	B	21	27	31
2	2018	4	no	B	28	0	23
2	2018	4	no	B	31	2	32
2	2018	4	no	B	32	28	23
2	2018	4	no	C	19	25	19
2	2018	4	no	C	22	3	25
2	2018	4	no	C	25	1	39
2	2018	4	no	C	29	3	30
2	2018	4	yes	A	3	47	51
2	2018	4	yes	A	10	6	23
2	2018	4	yes	A	13	7	41
2	2018	4	yes	A	14	0	25
2	2018	4	yes	B	6	3	26
2	2018	4	yes	B	8	1	32
2	2018	4	yes	B	12	19	28
2	2018	4	yes	B	15	0	32
2	2018	4	yes	C	1	1	12
2	2018	4	yes	C	2	3	39
2	2018	4	yes	C	5	1	36
2	2018	4	yes	C	9	1	36
2	2019	5	no	A	18	0	10
2	2019	5	no	A	23	5	21
2	2019	5	no	A	27	12	26
2	2019	5	no	A	31	0	11
2	2019	5	no	B	17	0	26
2	2019	5	no	B	21	0	21
2	2019	5	no	B	28	1	14
2	2019	5	no	B	29	2	13
2	2019	5	no	C	19	1	8
2	2019	5	no	C	20	0	17
2	2019	5	no	C	22	4	6
2	2019	5	no	C	24	4	16
2	2019	5	yes	A	1	0	14
2	2019	5	yes	A	6	1	21
2	2019	5	yes	A	10	0	9
2	2019	5	yes	A	14	2	4
2	2019	5	yes	B	3	0	14
2	2019	5	yes	B	11	1	13
2	2019	5	yes	B	12	3	6
2	2019	5	yes	B	16	2	7
2	2019	5	yes	C	2	1	7
2	2019	5	yes	C	4	2	8
2	2019	5	yes	C	7	1	7
2	2019	5	yes	C	9	0	7
2	2020	6	no	A	23	3	32
2	2020	6	no	A	24	41	35
2	2020	6	no	A	29	2	4
2	2020	6	no	A	31	0	6
2	2020	6	no	B	17	0	0
2	2020	6	no	B	21	0	24
2	2020	6	no	B	27	16	21
2	2020	6	no	B	30	3	56
2	2020	6	no	C	22	15	40
2	2020	6	no	C	26	18	38
2	2020	6	no	C	28	2	43
2	2020	6	no	C	32	9	41
2	2020	6	yes	A	9	0	68
2	2020	6	yes	A	10	7	50
2	2020	6	yes	A	15	0	22
2	2020	6	yes	A	16	0	25
2	2020	6	yes	B	4	0	60
2	2020	6	yes	B	5	2	34
2	2020	6	yes	B	7	0	38
2	2020	6	yes	B	11	20	39
2	2020	6	yes	C	1	0	23
2	2020	6	yes	C	3	0	36
2	2020	6	yes	C	8	1	47
2	2020	6	yes	C	13	3	54
2	2019	7	no	A	18	0	44
2	2019	7	no	A	25	2	38
2	2019	7	no	A	26	0	33
2	2019	7	no	A	32	0	32
2	2019	7	no	B	23	0	17
2	2019	7	no	B	24	0	64
2	2019	7	no	B	27	5	43
2	2019	7	no	B	28	1	38
2	2019	7	no	C	17	1	28
2	2019	7	no	C	19	0	35
2	2019	7	no	C	20	10	37
2	2019	7	no	C	29	5	31
2	2019	7	yes	A	12	0	21
2	2019	7	yes	A	13	3	21
2	2019	7	yes	A	15	2	47
2	2019	7	yes	A	16	2	50
2	2019	7	yes	B	1	1	50
2	2019	7	yes	B	2	4	43
2	2019	7	yes	B	3	0	49
2	2019	7	yes	B	8	0	57
2	2019	7	yes	C	4	1	63
2	2019	7	yes	C	5	2	41
2	2019	7	yes	C	7	1	31
2	2019	7	yes	C	10	3	28
2	2020	8	no	A	17	0	24
2	2020	8	no	A	26	6	21
2	2020	8	no	A	28	1	56
2	2020	8	no	A	32	4	40
2	2020	8	no	B	20	2	38
2	2020	8	no	B	22	1	43
2	2020	8	no	B	25	0	41
2	2020	8	no	B	30	1	68
2	2020	8	no	C	19	0	50
2	2020	8	no	C	24	0	22
2	2020	8	no	C	27	2	25
2	2020	8	no	C	29	11	60
2	2020	8	yes	A	2	9	34
2	2020	8	yes	A	6	6	38
2	2020	8	yes	A	12	8	39
2	2020	8	yes	A	14	0	23
2	2020	8	yes	B	5	0	36
2	2020	8	yes	B	8	0	47
2	2020	8	yes	B	11	0	54
2	2020	8	yes	B	15	0	9
2	2020	8	yes	C	3	1	20
2	2020	8	yes	C	4	0	23
2	2020	8	yes	C	10	1	46
2	2020	8	yes	C	16	0	17
2	2018	9	no	A	21	16	56
2	2018	9	no	A	23	0	34
2	2018	9	no	A	26	2	38
2	2018	9	no	A	29	0	32
2	2018	9	no	B	18	19	66
2	2018	9	no	B	20	5	68
2	2018	9	no	B	25	5	25
2	2018	9	no	B	28	4	16
2	2018	9	no	C	19	7	23
2	2018	9	no	C	22	3	11
2	2018	9	no	C	31	1	25
2	2018	9	no	C	32	25	62
2	2018	9	yes	A	2	0	38
2	2018	9	yes	A	4	0	39
2	2018	9	yes	A	6	0	56
2	2018	9	yes	A	10	0	39
2	2018	9	yes	B	7	13	51
2	2018	9	yes	B	11	2	36
2	2018	9	yes	B	15	1	52
2	2018	9	yes	B	16	1	49
2	2018	9	yes	C	3	2	18
2	2018	9	yes	C	5	1	19
2	2018	9	yes	C	9	3	41
2	2018	9	yes	C	13	13	69
2	2019	10	no	A	23	3	5
2	2019	10	no	A	24	1	1
2	2019	10	no	A	26	0	13
2	2019	10	no	A	32	3	3
2	2019	10	no	B	18	0	0
2	2019	10	no	B	19	0	7
2	2019	10	no	B	25	0	6
2	2019	10	no	B	29	0	7
2	2019	10	no	C	17	1	3
2	2019	10	no	C	21	1	4
2	2019	10	no	C	28	3	6
2	2019	10	no	C	31	4	7
2	2019	10	yes	A	6	0	9
2	2019	10	yes	A	10	0	7
2	2019	10	yes	A	13	5	4
2	2019	10	yes	A	14	3	9
2	2019	10	yes	B	1	2	4
2	2019	10	yes	B	2	2	3
2	2019	10	yes	B	4	5	21
2	2019	10	yes	B	16	0	5
2	2019	10	yes	C	3	0	4
2	2019	10	yes	C	7	0	7
2	2019	10	yes	C	9	0	0
2	2019	10	yes	C	11	0	6
3	2019	1	no	A	21	0	7
3	2019	1	no	A	25	10	5
3	2019	1	no	A	29	2	4
3	2019	1	no	A	32	2	5
3	2019	1	no	B	19	2	5
3	2019	1	no	B	22	7	14
3	2019	1	no	B	23	4	2
3	2019	1	no	B	30	2	5
3	2019	1	no	C	24	0	12
3	2019	1	no	C	26	9	9
3	2019	1	no	C	28	4	8
3	2019	1	no	C	31	2	3
3	2019	1	yes	A	5	3	4
3	2019	1	yes	A	6	8	4
3	2019	1	yes	A	7	0	3
3	2019	1	yes	A	10	2	7
3	2019	1	yes	B	3	3	5
3	2019	1	yes	B	4	0	14
3	2019	1	yes	B	12	1	10
3	2019	1	yes	B	16	0	8
3	2019	1	yes	C	2	2	4
3	2019	1	yes	C	9	1	9
3	2019	1	yes	C	14	1	14
3	2019	1	yes	C	15	14	11
3	2021	2	no	A	20	0	36
3	2021	2	no	A	21	0	43
3	2021	2	no	A	29	0	17
3	2021	2	no	A	32	0	49
3	2021	2	no	B	23	0	19
3	2021	2	no	B	24	0	30
3	2021	2	no	B	28	0	28
3	2021	2	no	B	31	0	41
3	2021	2	no	C	17	0	25
3	2021	2	no	C	18	1	20
3	2021	2	no	C	22	0	41
3	2021	2	no	C	26	0	33
3	2021	2	yes	A	10	0	25
3	2021	2	yes	A	12	0	29
3	2021	2	yes	A	13	0	14
3	2021	2	yes	A	15	0	12
3	2021	2	yes	B	3	1	32
3	2021	2	yes	B	6	0	25
3	2021	2	yes	B	9	0	47
3	2021	2	yes	B	14	0	32
3	2021	2	yes	C	2	0	49
3	2021	2	yes	C	8	0	30
3	2021	2	yes	C	11	0	20
3	2021	2	yes	C	16	0	4
3	2019	3	no	A	17	5	4
3	2019	3	no	A	24	1	2
3	2019	3	no	A	25	2	3
3	2019	3	no	A	32	3	4
3	2019	3	no	B	18	1	5
3	2019	3	no	B	29	1	1
3	2019	3	no	B	30	0	2
3	2019	3	no	B	31	3	0
3	2019	3	no	C	20	13	8
3	2019	3	no	C	23	1	3
3	2019	3	no	C	27	2	0
3	2019	3	no	C	28	2	2
3	2019	3	yes	A	4	3	10
3	2019	3	yes	A	14	1	2
3	2019	3	yes	A	15	0	0
3	2019	3	yes	A	16	0	0
3	2019	3	yes	B	5	2	3
3	2019	3	yes	B	9	0	0
3	2019	3	yes	B	12	0	1
3	2019	3	yes	B	13	0	0
3	2019	3	yes	C	1	13	3
3	2019	3	yes	C	7	2	2
3	2019	3	yes	C	8	0	0
3	2019	3	yes	C	10	0	5
3	2019	4	no	A	17	1	31
3	2019	4	no	A	20	0	30
3	2019	4	no	A	26	2	26
3	2019	4	no	A	27	1	43
3	2019	4	no	B	21	6	30
3	2019	4	no	B	28	0	29
3	2019	4	no	B	31	4	47
3	2019	4	no	B	32	9	45
3	2019	4	no	C	19	3	18
3	2019	4	no	C	22	0	30
3	2019	4	no	C	25	1	41
3	2019	4	no	C	29	0	45
3	2019	4	yes	A	3	4	53
3	2019	4	yes	A	10	3	25
3	2019	4	yes	A	13	3	53
3	2019	4	yes	A	14	2	43
3	2019	4	yes	B	6	0	35
3	2019	4	yes	B	8	0	35
3	2019	4	yes	B	12	1	40
3	2019	4	yes	B	15	0	42
3	2019	4	yes	C	1	0	19
3	2019	4	yes	C	2	5	48
3	2019	4	yes	C	5	0	54
3	2019	4	yes	C	9	0	41
3	2020	5	no	A	18	5	11
3	2020	5	no	A	23	15	25
3	2020	5	no	A	27	22	25
3	2020	5	no	A	31	9	16
3	2020	5	no	B	17	40	21
3	2020	5	no	B	21	8	10
3	2020	5	no	B	28	5	8
3	2020	5	no	B	29	6	8
3	2020	5	no	C	19	6	8
3	2020	5	no	C	20	6	17
3	2020	5	no	C	22	25	6
3	2020	5	no	C	24	16	16
3	2020	5	yes	A	1	0	11
3	2020	5	yes	A	6	0	23
3	2020	5	yes	A	10	3	6
3	2020	5	yes	A	14	5	5
3	2020	5	yes	B	3	18	14
3	2020	5	yes	B	11	0	5
3	2020	5	yes	B	12	7	5
3	2020	5	yes	B	16	9	3
3	2020	5	yes	C	2	4	7
3	2020	5	yes	C	4	9	4
3	2020	5	yes	C	7	5	8
3	2020	5	yes	C	9	1	7
3	2021	6	no	A	23	4	35
3	2021	6	no	A	24	30	39
3	2021	6	no	A	29	4	7
3	2021	6	no	A	31	0	4
3	2021	6	no	B	17	0	5
3	2021	6	no	B	21	0	6
3	2021	6	no	B	27	15	31
3	2021	6	no	B	30	3	19
3	2021	6	no	C	22	9	25
3	2021	6	no	C	26	13	19
3	2021	6	no	C	28	2	22
3	2021	6	no	C	32	2	50
3	2021	6	yes	A	9	1	13
3	2021	6	yes	A	10	5	16
3	2021	6	yes	A	15	1	16
3	2021	6	yes	A	16	0	25
3	2021	6	yes	B	4	0	9
3	2021	6	yes	B	5	4	17
3	2021	6	yes	B	7	1	15
3	2021	6	yes	B	11	5	21
3	2021	6	yes	C	1	1	26
3	2021	6	yes	C	3	0	6
3	2021	6	yes	C	8	0	21
3	2021	6	yes	C	13	1	26
3	2020	7	no	A	18	0	9
3	2020	7	no	A	25	3	20
3	2020	7	no	A	26	1	23
3	2020	7	no	A	32	2	46
3	2020	7	no	B	23	1	17
3	2020	7	no	B	24	0	60
3	2020	7	no	B	27	0	39
3	2020	7	no	B	28	4	26
3	2020	7	no	C	17	5	34
3	2020	7	no	C	19	1	35
3	2020	7	no	C	20	7	43
3	2020	7	no	C	29	1	33
3	2020	7	yes	A	12	0	24
3	2020	7	yes	A	13	2	26
3	2020	7	yes	A	15	0	43
3	2020	7	yes	A	16	6	43
3	2020	7	yes	B	1	1	44
3	2020	7	yes	B	2	1	40
3	2020	7	yes	B	3	0	47
3	2020	7	yes	B	8	2	46
3	2020	7	yes	C	4	1	60
3	2020	7	yes	C	5	2	37
3	2020	7	yes	C	7	2	27
3	2020	7	yes	C	10	7	26
3	2021	8	no	A	17	0	35
3	2021	8	no	A	26	1	22
3	2021	8	no	A	28	0	51
3	2021	8	no	A	32	0	42
3	2021	8	no	B	20	0	37
3	2021	8	no	B	22	1	37
3	2021	8	no	B	25	0	37
3	2021	8	no	B	30	1	62
3	2021	8	no	C	19	0	42
3	2021	8	no	C	24	0	34
3	2021	8	no	C	27	2	29
3	2021	8	no	C	29	7	59
3	2021	8	yes	A	2	4	35
3	2021	8	yes	A	6	1	42
3	2021	8	yes	A	12	9	39
3	2021	8	yes	A	14	0	29
3	2021	8	yes	B	5	0	38
3	2021	8	yes	B	8	0	41
3	2021	8	yes	B	11	0	48
3	2021	8	yes	B	15	0	24
3	2021	8	yes	C	3	0	36
3	2021	8	yes	C	4	0	35
3	2021	8	yes	C	10	1	52
3	2021	8	yes	C	16	0	31
3	2019	9	no	A	21	6	56
3	2019	9	no	A	23	0	34
3	2019	9	no	A	26	1	38
3	2019	9	no	A	29	0	32
3	2019	9	no	B	18	8	66
3	2019	9	no	B	20	0	68
3	2019	9	no	B	25	3	25
3	2019	9	no	B	28	0	16
3	2019	9	no	C	19	0	23
3	2019	9	no	C	22	0	11
3	2019	9	no	C	31	1	25
3	2019	9	no	C	32	5	62
3	2019	9	yes	A	2	0	38
3	2019	9	yes	A	4	0	39
3	2019	9	yes	A	6	0	56
3	2019	9	yes	A	10	0	39
3	2019	9	yes	B	7	0	51
3	2019	9	yes	B	11	0	36
3	2019	9	yes	B	15	0	52
3	2019	9	yes	B	16	2	49
3	2019	9	yes	C	3	1	18
3	2019	9	yes	C	5	1	19
3	2019	9	yes	C	9	0	41
3	2019	9	yes	C	13	4	69
3	2020	10	no	A	23	1	4
3	2020	10	no	A	24	0	0
3	2020	10	no	A	26	0	8
3	2020	10	no	A	32	5	4
3	2020	10	no	B	18	0	0
3	2020	10	no	B	19	0	9
3	2020	10	no	B	25	0	3
3	2020	10	no	B	29	0	3
3	2020	10	no	C	17	0	3
3	2020	10	no	C	21	0	1
3	2020	10	no	C	28	1	11
3	2020	10	no	C	31	0	10
3	2020	10	yes	A	6	0	11
3	2020	10	yes	A	10	1	10
3	2020	10	yes	A	13	2	5
3	2020	10	yes	A	14	1	7
3	2020	10	yes	B	1	0	5
3	2020	10	yes	B	2	1	6
3	2020	10	yes	B	4	0	30
3	2020	10	yes	B	16	2	1
3	2020	10	yes	C	3	1	3
3	2020	10	yes	C	7	0	7
3	2020	10	yes	C	9	0	0
3	2020	10	yes	C	11	0	1
;
run;

proc glimmix method = laplace data = exper1;
  class SITE Herb veg time plot;
  model count = herb|veg|time / dist=negbin link=log;
random site year site*year*time / subject= site*herb*veg type=ar(1);
run;

First, I coded my random statement accordingly for a staggered start design with random block and year effects, shown as “random site year site*year*time:, but this is for a design WITHOUT replication within block. But I’m having difficulty understanding how to incorporate random plot effects, as I can’t find guidance on the SAS rules for pooling effects when my design has replication within site as well as the other sources of variation.
Second, I want to compare this Herb|Veg|Time model with a model that uses a covariate measured at the plot level in each year (Covar) to see if it is a better model than the previous model (comparison of model AICCs). I expect this covariate may be a good explanation for the year effect, and it has mechanistic importance that is more informative. I think the following SAS code is appropriate:

model count=herb veg Covar*herb Covar*veg time time*herb time*veg;
random site / subject=site*herb*veg type=ar(1);

I am hopeful someone can assist with my questions about the SAS code for this design. Thank you for assistance and insights.

[Ksharp]

You should post it at Statistic Forum
https://communities.sas.com/t5/Statistical-Procedures/bd-p/statistical_procedures
And calling stat expert @StatDave @StatsMan @SteveDenham @StatsMan

[SteveDenham]

I think we can address most of your questions by rearranging some of the code. It appears to me that you have 3 fixed effect design factors implemented for each plot within each site. If that is the case, then the following would be my first attempt:

proc glimmix /*method = laplace*/ data = exper1;
class SITE Herb veg time plot year;
nloptions maxiter=5000;
model count = herb|veg|time / dist=negbin link=log ddfm=kr2;
random intercept plot/ subject=site;
random year / subject= plot(site) type=cs;
run;

This nests plots within each year. The issue here that needs some clarification is whether the plots are identical within site from year to year. The code above assumes that they are. If not, the easiest thing to do would be to recode the plots so that they are unique across site and year. Since not all plots within a site. were measured on all years. Some changes made were to use the default pseudo-likelihood method of optimization rather than the Laplace integration, and to specify the type of covariance structure for year as compound symmetric as at most 2 years were available for estimation on any plot.

SteveDenham

[Lesley6145]

Thank you for your response. Yes, indeed there are three fixed factors (Herb, Veg, and Time-since-treatment). Regarding clarification: The plots number from 1-24 within each site corresponding to the 2 Herb x 3 Veg x 4 replicate combinations; these combinations were randomly assigned within each site so plot numbers do not necessarily correspond to the same treatment combinations. The same plot number in a site does correspond to counts for that plot in year 2 and year 3.  I think that is consistent with what you mean by “identical within site from year to year”.

In running your recommended code, it is making some sense to me how you rearranged the random statements. The default pseudo-likelihood method of optimization however does not generate AICC so I am unable to conduct model selection (i.e., comparison of full model herb|veg|time versus herb|time, herb time, veg|time, etc.) to rank plausible models. Is there a rationale why Laplace integration is inappropriate here? It does allow model selection in this fashion, but with your new code Laplace provides F-stats/Pvalues for all terms except those with Time, and the error “Estimated G matrix is not positive definite”.  

In addition to this set of models, I am also trying to include models that contain covariates to serve in lieu of the random effects of year, year*herb, and year*veg. The covariate “shrub” is one such covariate that may influence seedling counts, and it was measured on each plot in each year. So, for example:

count = herb veg shrub*herb shrub*veg time herb*time veg*time herb*veg*time

With year effects now substituted by the shrub covariate, I assume I only maintain the “random intercept plot / subject=site;” for this type of model?

[SteveDenham]

With regards to this question: Is there a rationale why Laplace integration is inappropriate here? It does allow model selection in this fashion, but with your new code Laplace provides F-stats/Pvalues for all terms except those with Time, and the error “Estimated G matrix is not positive definite”

The missing F stats and the Estimated G matrix statements point to an issue that the model is too complex to fit with this amount of data and a single point quadrature. My normal reaction there is to drop back to RSPL methods, and sacrifice IC calculations. One thing you might try is method=quad(fastquad). I am not up to speed on using that option yet, so it didn't occur to me that it might help. When I try, I get an ERROR: Insufficient resources to perform adaptive quadrature with 3 quadrature points. METHOD=LAPLACE, corresponding to a single point, may provide a computationally less intensive possibility

If you have a cloud account, you might be able to increase your MEMSIZE to use this method.

Given that, you could try selecting a covariance structure based on the generalized chi-square/DF ratio. Look for the structure that minimizes the absolute value of ln(generalized chi-squared/DF). That would give the structure that results in the smallest amount of over- or under-dispersion (and no, I don't have a reference for that method, so it is pretty much an ad hoc kind of thing. Any structure selected that way is crucially dependent on the distribution/link used and conditional on the fixed effect solution.

On to the covariate shrub as a mediator that serves as a surrogate for year - here I believe you are correct. I would proceed with caution though, as I doubt the number of shrubs is a complete surrogate for the year effect. Right now I am trying to fit a spline to the variable covar as maybe something better, but it is slow going.

SteveDenham