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lmer(Group_DV1 ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj) + (1|Group:Session_ID:Subj:CounterBalance), data = data))
lmer(Group_DV1 ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj), data = data))
lmer ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj) + (1|Group:Session_ID:Subj:CounterBalance), data = data)
lmer ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj), data = data)
lmer(Group_DV1 ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj) + (1|Group:Session_ID:Subj:CounterBalance), data = data))
lmer(Group_DV1 ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj), data = data))
tibble [54 x 9] (S3: tbl_df/tbl/data.frame)
$ Group : Factor w/ 3 levels "1","2","3": Grouping Factor
$ Subj : Factor w/ 3 levels "1","2","3": Subject IDs, nested in Group
$ CounterBalance: Factor w/ 3 levels "A","B","C": Counterbalance of first repeated measure (A = Condition A)
$ Session_ID : Factor w/ 2 levels "1","2": Measurement Session (3+ in real data). Each session consits of each counterbalance condition
$ Group_IV1 : num [1:54] IV measured at the group level. Hence ach subj has the same value for the group
$ Group_IV2 : num [1:54] Same as above but second IV
$ Subj_IV1 : num [1:54] IV measured at the subject level. Each counterbalance has the same value
$ Subj_IV2 : num [1:54] Same as above for second subject level ID
$ Group_DV : num [0[1:1.9]54] Group level DV. This DV was measured at the group level
Group Subj CounterBalance Session_ID Group_IV1 Group_IV2 Subj_IV1 Subj_IV2 Group_DV
<fct> <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 1 A 1 44 5 6 5 0.676
2 1 1 B 1 25 24 6 5 0.242
3 1 1 C 1 28 28 6 5 0.406
4 1 2 A 1 44 5 6 6 0.676
5 1 2 B 1 25 24 6 6 0.242
6 1 2 C 1 28 28 6 6 0.406
7 1 3 A 1 44 5 5 5 0.676
8 1 3 B 1 25 24 5 5 0.242
9 1 3 C 1 28 28 5 5 0.406
10 2 1 A 1 15 221 6 6 0.122
11 2 1 B 1 26 251 6 6 0.690
12 2 1 C 1 29 211 6 6 1.70
13 2 2 A 1 15 221 6 6 0.122
14 2 2 B 1 26 251 6 6 0.690
15 2 2 C 1 29 211 6 6 1.70
16 2 3 A 1 15 221 6 6 0.122
17 2 3 B 1 26 251 6 6 0.690
18 2 3 C 1 29 211 6 6 1.70
tibble [54 x 9] (S3: tbl_df/tbl/data.frame)
$ Group : Factor w/ 3 levels "1","2","3": Grouping Factor
$ Subj : Factor w/ 3 levels "1","2","3": Subject IDs, nested in Group
$ CounterBalance: Factor w/ 3 levels "A","B","C": Counterbalance of first repeated measure (A = Condition A)
$ Session_ID : Factor w/ 2 levels "1","2": Measurement Session (3+ in real data). Each session consits of each counterbalance condition
$ Group_IV1 : num [1:54] IV measured at the group level. Hence ach subj has the same value for the group
$ Group_IV2 : num [1:54] Same as above but second IV
$ Subj_IV1 : num [1:54] IV measured at the subject level. Each counterbalance has the same value
$ Subj_IV2 : num [1:54] Same as above for second subject level ID
$ Group_DV : num [0:1.9] Group level DV. This DV was measured at the group level
Group Subj CounterBalance Session_ID Group_IV1 Group_IV2 Subj_IV1 Subj_IV2 Group_DV
<fct> <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 1 A 1 44 5 6 5 0.676
2 1 1 B 1 25 24 6 5 0.242
3 1 1 C 1 28 28 6 5 0.406
4 1 2 A 1 44 5 6 6 0.676
5 1 2 B 1 25 24 6 6 0.242
6 1 2 C 1 28 28 6 6 0.406
7 1 3 A 1 44 5 5 5 0.676
8 1 3 B 1 25 24 5 5 0.242
9 1 3 C 1 28 28 5 5 0.406
10 2 1 A 1 15 221 6 6 0.122
11 2 1 B 1 26 251 6 6 0.690
12 2 1 C 1 29 211 6 6 1.70
13 2 2 A 1 15 221 6 6 0.122
14 2 2 B 1 26 251 6 6 0.690
15 2 2 C 1 29 211 6 6 1.70
16 2 3 A 1 15 221 6 6 0.122
17 2 3 B 1 26 251 6 6 0.690
18 2 3 C 1 29 211 6 6 1.70
tibble [54 x 9] (S3: tbl_df/tbl/data.frame)
$ Group : Factor w/ 3 levels "1","2","3": Grouping Factor
$ Subj : Factor w/ 3 levels "1","2","3": Subject IDs, nested in Group
$ CounterBalance: Factor w/ 3 levels "A","B","C": Counterbalance of first repeated measure (A = Condition A)
$ Session_ID : Factor w/ 2 levels "1","2": Measurement Session (3+ in real data). Each session consits of each counterbalance condition
$ Group_IV1 : num [1:54] IV measured at the group level. Hence ach subj has the same value for the group
$ Group_IV2 : num [1:54] Same as above but second IV
$ Subj_IV1 : num [1:54] IV measured at the subject level. Each counterbalance has the same value
$ Subj_IV2 : num [1:54] Same as above for second subject level ID
$ Group_DV : num [1:54] Group level DV. This DV was measured at the group level
Group Subj CounterBalance Session_ID Group_IV1 Group_IV2 Subj_IV1 Subj_IV2 Group_DV
<fct> <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 A 1 44 5 6 5 0.676
1 1 B 1 25 24 6 5 0.242
1 1 C 1 28 28 6 5 0.406
1 2 A 1 44 5 6 6 0.676
1 2 B 1 25 24 6 6 0.242
1 2 C 1 28 28 6 6 0.406
1 3 A 1 44 5 5 5 0.676
1 3 B 1 25 24 5 5 0.242
1 3 C 1 28 28 5 5 0.406
2 1 A 1 15 221 6 6 0.122
2 1 B 1 26 251 6 6 0.690
2 1 C 1 29 211 6 6 1.70
2 2 A 1 15 221 6 6 0.122
2 2 B 1 26 251 6 6 0.690
2 2 C 1 29 211 6 6 1.70
2 3 A 1 15 221 6 6 0.122
2 3 B 1 26 251 6 6 0.690
2 3 C 1 29 211 6 6 1.70
Prior Searches
Prior to reading below, I have searched this forum for other posts of this nature. I have a found a few, but I have not found them to be helpful to my specific challenge. Particularly, Dr. Bolker's response to this post was helpful in understanding a double repeated measures LMM. However, it did not help me understand how to tackle this challenge as my repeated measures are nested in both the subjects and their groups
Intro
I'm conducting a linear fixed effects model on multilevel data (Groups:Subjects) and two repeated measurements (Condition and Study Session). Each group and their respective subjects are measured over multiple data collection sessions (Session_ID). Each data collection session consists of three study conditions with the same group and their respective subjects. I have 2 group level measurements (e.g., group performance) and two subject level measurements (e.g., subject demographics). My subsequent DV is also measured at the group level. The problem I am facing here is that I do not know how to account for the repeated measure nature of the data set for both my data colleciton session and my counterbalanced condition while considering the nested structure of my data. I've attempted to replicate my code, but it is beyond my knowledge of R. Instead, I am providing a dput() of a toy data set that replicates my actual data set structure and will further explain my actual data set below.
Data
My variables are as follows:
tibble [54 x 9] (S3: tbl_df/tbl/data.frame)
$ Group : Factor w/ 3 levels "1","2","3": Grouping Factor
$ Subj : Factor w/ 3 levels "1","2","3": Subject IDs, nested in Group
$ CounterBalance: Factor w/ 3 levels "A","B","C": Counterbalance of first repeated measure (A = Condition A)
$ Session_ID : Factor w/ 2 levels "1","2": Measurement Session (3+ in real data). Each session consits of each counterbalance condition
$ Group_IV1 : num [1:54] IV measured at the group level. Hence ach subj has the same value for the group
$ Group_IV2 : num [1:54] Same as above but second IV
$ Subj_IV1 : num [1:54] IV measured at the subject level. Each counterbalance has the same value
$ Subj_IV2 : num [1:54] Same as above for second subject level ID
$ Group_DV : num [0:1.9] Group level DV. This DV was measured at the group level
Thus, as an example, my data looks like this:
Group Subj CounterBalance Session_ID Group_IV1 Group_IV2 Subj_IV1 Subj_IV2 Group_DV
<fct> <fct> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 1 A 1 44 5 6 5 0.676
2 1 1 B 1 25 24 6 5 0.242
3 1 1 C 1 28 28 6 5 0.406
4 1 2 A 1 44 5 6 6 0.676
5 1 2 B 1 25 24 6 6 0.242
6 1 2 C 1 28 28 6 6 0.406
7 1 3 A 1 44 5 5 5 0.676
8 1 3 B 1 25 24 5 5 0.242
9 1 3 C 1 28 28 5 5 0.406
10 2 1 A 1 15 221 6 6 0.122
11 2 1 B 1 26 251 6 6 0.690
12 2 1 C 1 29 211 6 6 1.70
13 2 2 A 1 15 221 6 6 0.122
14 2 2 B 1 26 251 6 6 0.690
15 2 2 C 1 29 211 6 6 1.70
16 2 3 A 1 15 221 6 6 0.122
17 2 3 B 1 26 251 6 6 0.690
18 2 3 C 1 29 211 6 6 1.70
*Notice the repeating data based on group, counterbalance, subj.
I am attempting to specify this type of model, fully, using a linear mixed model approach. However, I'm having a difficult time finding any material or sources that specify how to parameterize a multilevel model with two nested repeated measurements. Below, I will describe my though process that I have taken and try to explain where I'm confused.
Approach
So far, my approach has been to nest each repeated measure into their respective level and then nest each subj into their groups. This approach was derived from the logic presented in Raudenbush (2004) which states that repeated measures are nested within subjects. Thus, If I extend this approach to my hypothesized data structure I would say that my counterbalanced conditions (level 1) are nested within my subjects (level 2) who are nested within my data collection sessions (level 3) which are then nested within the groups (level 4):
CounterBalanced Condition > Subjects > Data Collection Session > Groups.
Thus, my syntax, I believe, would be:
lmer ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj) + (1|Group:Session_ID:Subj:CounterBalance), data = data)
However, this model specification leads to the following error:
Error: number of levels of each grouping factor must be < number of observations (problems: Group:Session_ID:Subj:CounterBalance)
Which I'm assuming to mean that I am nesting too many variable and have more neted levels than observations. But, since this is how the data is setup, I'm not sure how that could be the case?
In removing the counterbalance from the random effects, I am able to successfully run the model
lmer ~ Group_IV1 + Group_IV2 + SubjIV1 + Subj_IV2 + (1|Group) + (1|Group:Session_ID) + (1|Group:Session_ID:Subj), data = data)
But, I then run into a singularity as my random effects report that my Group:Session_ID:Subj has a variance of 0. Is this because there truly is no variance between subjects when accounting for the nesting or is because this model is specified incorrectly?
boundary (singular) fit: see ?isSingular
Linear mixed model fit by REML ['lmerModLmerTest']
Formula:
Group_DV ~ Group_IV1 + Group_IV2 + Subj_IV1 + Subj_IV2 + (1 |
Group) + (1 | Group:Session_ID) + (1 | Group:Session_ID:Subj)
Data: data
REML criterion at convergence: 53.873
Random effects:
Groups Name Std.Dev.
Group:Session_ID:Subj (Intercept) 0.0000
Group:Session_ID (Intercept) 0.2053
Group (Intercept) 0.3365
Residual 0.2914
Number of obs: 54, groups:
Group:Session_ID:Subj, 18; Group:Session_ID, 6; Group, 3
Fixed Effects:
(Intercept) Group_IV1 Group_IV2 Subj_IV1 Subj_IV2
-0.857832 0.046202 0.017655 -0.001838 -0.002266
optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
Any help in figuring out how to correctly specify this is appreciated.
*Replicatable Toy Dataset
My real dataset is roughly 1000 rows. I do not have the knowledge or skill level in R to replicate this data structure using code.
structure(list(Group = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L), .Label = c("1",
"2", "3"), class = "factor"), Subj = structure(c(1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L,
1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L,
3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L), .Label = c("1", "2", "3"), class = "factor"), CounterBalance = structure(c(1L,
2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L,
3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L,
1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 3L, 1L,
2L, 3L, 1L, 2L, 3L), .Label = c("A", "B", "C"), class = "factor"),
Session_ID = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L), .Label = c("1", "2"), class = "factor"), Group_IV1 = c(44,
25, 28, 44, 25, 28, 44, 25, 28, 15, 26, 29, 15, 26, 29, 15,
26, 29, 31, 20, 24, 31, 20, 24, 31, 20, 24, 30, 26, 21, 30,
26, 21, 30, 26, 21, 14, 18, 25, 14, 18, 25, 14, 18, 25, 27,
24, 26, 27, 24, 26, 27, 24, 26), Group_IV2 = c(5, 24, 28,
5, 24, 28, 5, 24, 28, 22, 25, 21, 22, 25, 21, 22, 25, 21,
0, 27, 28, 0, 27, 28, 0, 27, 28, 25, 26, 25, 25, 26, 25,
25, 26, 25, 19, 30, 21, 19, 30, 21, 19, 30, 21, 18, 24, 25,
18, 24, 25, 18, 24, 25), Subj_IV1 = c(6, 6, 6, 6, 6, 6, 5,
5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 6, 6, 6, 7, 7,
7, 5, 5, 5, 6, 6, 6, 5, 5, 5, 6, 6, 6, 5, 5, 5, 7, 7, 7,
6, 6, 6, 6, 6, 6, 6, 6, 6), Subj_IV2 = c(5, 5, 5, 6, 6, 6,
5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5,
5, 5, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 5, 5,
5, 7, 7, 7, 6, 6, 6, 6, 6, 6), Group_DV = c(0.67619, 0.24212,
0.40619, 0.67619, 0.24212, 0.40619, 0.67619, 0.24212, 0.40619,
0.1216, 0.68978, 1.70481, 0.1216, 0.68978, 1.70481, 0.1216,
0.68978, 1.70481, 0.34172, 0.00387, 0.92827, 0.34172, 0.00387,
0.92827, 0.34172, 0.00387, 0.92827, 0.48737, 0.66727, 0.78267,
0.48737, 0.66727, 0.78267, 0.48737, 0.66727, 0.78267, 0.8836,
0.82926, 1.23826, 0.8836, 0.82926, 1.23826, 0.8836, 0.82926,
1.23826, 0.58837, 0.53445, 0.87934, 0.58837, 0.53445, 0.87934,
0.58837, 0.53445, 0.87934)), row.names = c(NA, -54L), class = c("tbl_df",
"tbl", "data.frame"))
References
Raudenbush, S., Bryk, A., Cheong, Y. F., Congdon, R., & Toit, M. D. (n.d.). Conceptual and Statistical Background for Hierarchical Multivariate Linear Models. In HLM 6: Hierarchical linear and nonlinear modeling. essay, Scientific Software International.