# Specification of partially crossed longitudinal subjects in linear mixed effects model (lme4, lmer) [closed]

I am familiar with linear regression models, but I am in the process of learning about linear mixed effects models.

My data consists of measurements for each month for a set of subjects over a long period of time (~15 years). The subjects and time frames are partially crossed - subjects do not appear for each time point. I also have a number of covariates measured at the per date per subject level, and a single boolean variable indicating a whether a count is before or after a particular time point. The point of this particular model is to measure whether or not a particular event (occurring at the "mid date") had an effect on the count variable. Due to the partially crossed, longitudinal nature of my data and the general discontinuity of my data over time, I don't believe that simple paired t-tests can properly answer this question. My data frame is as follows:

head

   subject_id date_monthly count subject_join_date covar1_per_subject_per_date subject_group after_mid_date_bool covar2_per_subject_per_date covar3_per_subject_per_date
1:          0   2013-05-01     3        2011-07-01                           1     afteronly                TRUE                    22.33333                    195.7986
2:          0   2013-04-01     1        2011-07-01                           1     afteronly                TRUE                    21.33333                    194.7986
3:          0   2013-02-01    19        2011-07-01                           1     afteronly                TRUE                    19.36806                    192.8333
4:          0   2013-12-01     3        2011-07-01                           1     afteronly                TRUE                    29.46806                    202.9333
5:          0   2013-10-01     4        2011-07-01                           1     afteronly                TRUE                    27.43333                    200.8986


tail

       subject_id date_monthly count subject_join_date covar1_per_subject_per_date subject_group after_mid_date_bool covar2_per_subject_per_date covar3_per_subject_per_date
22407:       6911   2013-08-01     3        2011-08-01                           1     afteronly                TRUE                    24.36667                    198.8653
22408:       6911   2013-07-01     1        2011-08-01                           1     afteronly                TRUE                    23.33333                    197.8319
22409:       6911   2013-06-01     1        2011-08-01                           1     afteronly                TRUE                    22.33333                    196.8319
22410:       6931   2009-05-01     7        2009-05-01                           1    beforeonly               FALSE                     0.00000                    147.0986
22411:        238   2013-09-01     1        2012-10-01                           1     afteronly                TRUE                    11.16667                    199.8986


count is the response I am looking to model.

I've read through all of Bates' lme4 paper, but I am still confused as to how to specify the random effects part of my model.

My attempt at a model specification is:

lmer(log(count) ~ covar1_per_subject_per_date + covar2_per_subject_per_date +
covar3_per_subject_per_date + after_mid_date_bool +
subject_group + subject_join_date + (1|subject_id) + (1|date_monthly),
data=df, REML=F)


Which "works" (no errors from lmer). However, my primary question is:

Is this the correct specification for a mixed effects model with random, uncorrelated intercepts for subject_id and date_monthly? Correct here means that we model independent fixed effects for each of the fixed effects specified in the model, accounting for multiple trials of the same subject over time with subjects not appearing at every time point.

A secondary but related question is:

Have I organized my data frame in the proper way? My worry is that the after_mid_date column may be specified improperly.

I apologize if this is long-winded or too-specific of a question. My intention of providing my exact data is to be as clear as possible with my question.

## closed as off-topic by mkt, Juho Kokkala, Michael Chernick, Peter Flom♦Jan 16 at 10:52

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