I recently reviewed a paper that used Wald's Z in a mixed model
analysis. The dataset (see end of message for complete dataset) has
individual animals (SAMPLE) from within social groups, from within
geographic regions. Y is the response variable. The paper ran a mixed
model with year and region as fixed effects, group a random effect
nested within region, and sample nested within group. I found this
odd, as that leaves no information for an error term (there is no
replication within individual. The author wanted to determine what
fraction of the variation in Y was due to each of these terms, and of
greatest interest was whether there was appreciable
within-group (among Sample nested within group) variance. He/she
applied Wald's Z in SPSS, which provides estimates of variance
components as well as standard errors of these estimates. Wald's Z is
just an F statistic with the variance/se(variance).
Here are my two questions:
1) lacking access to Pinhero and Bates at the moment, what is the
appropriate model structure in lmer or nlme for this model (year and
region fixed, group random nested within fixed region effect, and
sample nested within group?
2) How can I obtain s.e(variance) to obtain Wald's Z?
Thanks!
-Dan Bolnick
SAMPLE REGION GROUP YEAR Y
1 IngM03BS-1 mainland Mystery 3 -23.68
2 IngM03BS02 mainland Mystery 3 -23.61
3 IngM03BS-04 mainland Mystery 3 -23.76
4 IngM02BS01 mainland Mystery 2 -23.61
5 IngM02BS02 mainland Mystery 2 -24.37
6 IngM02BS03 mainland Mystery 2 -23.93
7 Ing03BS05 mainland Mystery 3 -23.88
8 ELLM04BS03 mainland Mystery 4 -23.66
9 EllM04BS02 mainland Mystery 4 -23.59
10 CIM03BS01 mainland Mountain 3 -22.79
11 POWM03BS03 mainland Mountain 3 -21.08
12 POWM03BS02 mainland Mountain 3 -20.42
13 ClM01BS02 mainland Mountain 1 -20.81
14 CPM01BS01 mainland Mountain 1 -21.04
15 ClM01Ca01 mainland Mountain 1 -22.95
16 NK03BS04 mainland Mosquito 3 -23.01
17 NkM03BS02 mainland Mosquito 3 -23.45
18 ROSM03BS02 mainland BigCountry 3 -22.33
19 ROSM03BS03 mainland BigCountry 3 -23.61
20 ROSM03BS02 mainland BigCountry 3 -22.80
21 ROSMB03S01 mainland BigCountry 3 -22.96
22 AAM01Ca02 mainland Alice 1 -20.63
23 AAM01Ca03 mainland Alice 1 -20.83
24 ElM04Ca01 mainland Elcho 4 -21.11
25 YeI03BS05 innerislands Village 3 -19.82
26 YeI03BS01 innerislands Village 3 -18.07
27 YeI03BS04 innerislands Village 3 -20.70
28 YeI03BS03 innerislands Village 3 -19.37
29 YeI03BS06 innerislands Village 3 -21.14
30 YeI03BS02 innerislands Village 3 -21.25
31 YeI02BS02 innerislands Village 2 -20.98
32 YeI02BS04 innerislands Village 2 -20.40
33 YeI02BS05 innerislands Village 2 -19.96
34 YeI00BS01 innerislands Village 1 -23.34
35 YeI00BS02 innerislands Village 1 -23.06
36 YeI01DS01 innerislands Village 1 -22.10
37 YeI04BS02 innerislands Village 4 -20.81
38 YeI04S01T innerislands Village 4 -19.75
39 HuI04BS01 innerislands Ochre 4 -21.17
40 DeI03BS01 innerislands Local 3 -20.78
41 CaI03Ca01 innerislands Local 3 -22.59
42 ChI02BS01 innerislands Fishtrap 2 -17.73
43 ChI02BS02 innerislands Fishtrap 2 -18.24
44 ChI02BS03 innerislands Fishtrap 2 -18.74
45 ChI02DS01 innerislands Fishtrap 2 -19.23
46 ChI01BS05 innerislands Fishtrap 2 -16.78
47 ChI01DS01 innerislands Fishtrap 1 -21.17
48 ChI01DS02 innerislands Fishtrap 1 -20.70
49 ChI01DS03 innerislands Fishtrap 1 -21.07
50 ChI01HS01 innerislands Fishtrap 1 -19.07
51 ChI01BS01 innerislands Fishtrap 1 -21.53
52 ChI01BS03 innerislands Fishtrap 1 -18.32
53 ChI01BS05 innerislands Fishtrap 1 -17.32
54 ChI01BS06 innerislands Fishtrap 1 -18.39
55 CuII01BS01 innerislands Fishtrap 1 -23.48
56 CuII01BS02 innerislands Fishtrap 1 -22.82
57 CuII01BS03 innerislands Fishtrap 1 -22.19
58 SuI03BS01 innerislands Susan 3 -22.35
59 SuI03DS01 innerislands Susan 3 -21.70
60 SuI03BS02 innerislands Susan 3 -22.25
61 SuI04BS01 innerislands Susan 4 -22.57
62 SuI04BS02 innerislands Susan 4 -22.08
63 SuI04BS02 innerislands Susan 4 -21.73
64 PRI03BS01 innerislands Princess 3 -18.11
65 PRI03BS02 innerislands Princess 3 -21.59
66 HaI03BS03 innerislands Hawkesbury 3 -17.56
67 HaI03BS02 innerislands Hawkesbury 3 -17.68
68 HaI01BS01 innerislands Hawkesbury 1 -18.43
69 HaI01Ca01 innerislands Hawkesbury 1 -18.12
70 FiI01BS01 innerislands Fin 1 -21.92
71 GiI01BS01 outerislands Gil 1 -17.17
72 GiI01BS02 outerislands Gil 1 -18.21
73 GiI01BS05 outerislands Gil 1 -16.54
74 GiI01BS04 outerislands Gil 1 -17.47
75 GiI01BS03 outerislands Gil 1 -19.01
76 DuI03BS01 outerislands Dundas 3 -15.07
77 DuI03BS02 outerislands Dundas 3 -15.42
78 BaI03BS02 outerislands Banks 3 -18.50
