I am currently developing a demographic model to project the recovery of corals that were impacted by an oil spill. Corals have branches that can be three different states: healthy, unhealthy or colonized by other organisms. Every year each branch can transition to one of these three states or break. I have measured the proportion of branches that transitioned from one state to another for the same corals (close to a 100 corals) every year for 5 years and would like to use this data to parameterize my demographic model.
I initially tested the effect of three fixed variables (Initial impact, number of associates and coral size) on each transition with GLMM models using a binomial distribution (since I have proportion data - a transition occurs or not) and year of sampling. I ran separate glmm models for each transition. For instance for healthy branches I ran the following models:
> nv[1:4,]
Coral Total Total.nv nv_to_nv nv_to_nh nv_to_hy Impact Ophiuroid Size Site Year
1 A2 63 63 63 0 0 0.00000000 1 0.7850999 MC294 2011-2012
2 A6 204 201 199 0 0 0.01578898 1 2.8842783 MC294 2011-2012
3 A10 303 108 103 3 2 0.64293344 0 6.4493261 MC294 2011-2012
4 A14 38 36 36 0 0 0.05288091 0 1.1652219 MC294 2011-2012
Coral: Individual coral ID
Total.nv: total number of healthy branches
nv_to_nv: number of healthy branches that remained healthy
nv_to_nh: number of healthy branches that became unhealthy
nv_to_nv: number of healthy branches that became colonized by other organisms.
Impact: Proportion of branches initially impacted
yhh <- cbind(nv_to_nv, Total.nv - nv_to_nv)
modelhh<-glmer(yhh ~ Impact + (1 | Year) + (1 | Coral), family = binomial)
yhi <- cbind(nv_to_nh, Total.nv - nv_to_nh)
modelhi<-glmer(yhi ~ Impact + (1 | Year) + (1 | Coral), family = binomial)
yhhy <- cbind(nv_to_hy, Total.nv - nv_to_hy)
modelhhy<-glmer(yhhy ~ Impact + (1 | Year) + (1 | Coral), family = binomial)
I then used the predict() function to predict each transition independently for different values of Impact, and used these values for my demographic model.
I know this is inaccurate because I used separate glmms treating each transitions as if they were independent, which is not the case.
I think that I need to model these transitions using a multinomial distribution instead of binomial and I do not think that the lme4 package offers this option. I looked at the mlogit() and multinom() functions but none of them seem to allow for categorical random effects.
I found that multinomial glmms are possible with the MCMCglmm() function and I was wondering if anyone had experience using the predict() function with multinomial glmms.
I also considered modeling my transitions as a series of binomial models for each contrast (“Begg and Gray Approximation”). Then again I was wondering if it is possible to make predictions with this methods.
Thank you
Related
SUMMARY
I'm analyzing avian point count data using glmmTMB.
I'm trying to estimate year-specific mean abundance for each species.
Models with interactions of fixed terms are not working, I think because
limited data are split across several factors (species, year, week, site).
I'm wondering if adopting a random-effects parameterization is reasonable
(shrinking estimates to a realistic range)?
I'm seeking guidance on what the code for that parameterization would look like.
Any and all recommendations or lessons are greatly appreciated! Thank you.
Intro
The data.
I'm working on an analysis of a pre-existing database. The data are semi-structured, opportunistic observations of bird species abundance (zero-filled) collected via a stationary point count methodology. So, each species can be recorded at a site during a week of each year, but there are many "missing" observations since it's an opportunistic design. I'm looking for advice on modeling techniques, particularly related to random effects.
Modeling approach.
I want to estimate annual abundance for each species through a single model (akin to a multi-species, dynamic N-mix model, but assuming p = 1). Since the data are opportunistic counts, a zero-inflated and negative binomial model should make the most sense. Additionally, there is some pseudo-replication of counts at sites, so I know I need site as a random effect, e.g.: + (1|site). My understanding is that mgcv or glmmTMB are my best options for this type of modeling, and I know Gavin Simpson has mentioned that glmmTMB is likely preferable over mgcv when a factor used as a random effect has a large number (100s) of levels (here, 272 sites).
The issue
I've tried to use interaction effects comprised of fixed terms of species and year (similar to the Salamander example) to capture the species-specific annual estimates I'm interested in, but the model runs for hours, only to end up crashing. (Note: I can only get it to run & converge if I use a gaussian model, but I don't think that's reasonable given the data.) The terms week and year are factors (not integers) because I expect both to have non-linearity, which is important. Overall, I think there's not enough data for fully-independent estimates of these terms.
m0 <- glmmTMB(count ~ species*year + species*week + (1|site),
ziformula = ~ species,
family = nbinom2,
data = df)
Current direction
Random effects.
I've often been taught that random effects should only be used to try to eliminate effects that are not of interest, but I was digging into resources online and I came across some of Ben Bolker's writing, which included a discussion of how random effects can have a practical utility beyond stricter definitions. So, I tried switching from interaction effects to various random effect parameterizations, in hopes of allowing levels of species and years to borrow from each other (shrinkage to "population" average).
However, I've gotten a bit confused along the way and I could use some help from others who have more experience working with this type of data.
Starting over.
I'm trying to restart by going back to the essentials, focusing only on species-year estimation. When I include a simple random effect structure, such as (1|species) + (1|year), the model estimates the same trend for each species, only varying the intercept, whereas I want each species to be able to be totally different. I think I need some sort of crossed or nested structure, but in reading up on those I got a bit confused for this case (i.e., several schools with their own students makes more sense, with lots of examples and explanations!).
Currently working.
What I can get running is m1 below, which produces the estimates I want. but I'm not sure if it's justifiable, or if there's something better. I also need something that can include week and site, too.
m1 <- glmmTMB(count ~ (1|species) + (0+species|winter),
ziformula = ~ (1|species),
family = nbinom2,
data = df)
Data
I added the data to Google Drive, which can be downloaded from this link.
Data summary
Two representations of the same data:
# A tibble: 262,040 × 6
count species checklist site year week
<dbl> <chr> <fct> <fct> <fct> <fct>
1 0 American Crow C1262 S174 2020 5
2 0 American Goldfinch C1262 S174 2020 5
3 0 American Robin C1262 S174 2020 5
4 0 American Tree Sparrow C1262 S174 2020 5
5 2 Black-capped Chickadee C1262 S174 2020 5
6 0 Blue Jay C1262 S174 2020 5
7 0 Brown Creeper C1262 S174 2020 5
8 0 Brown-headed Cowbird C1262 S174 2020 5
9 0 Carolina Wren C1262 S174 2020 5
10 0 Cedar Waxwing C1262 S174 2020 5
# … with 262,030 more rows
'data.frame': 262040 obs. of 6 variables:
$ count : num 0 0 0 0 2 0 0 0 0 0 ...
$ species : chr "American Crow" "American Goldfinch" "American Robin" "American Tree Sparrow" ...
$ checklist: Factor w/ 6551 levels "C0001","C0002",..: 1262 1262 1262 1262 1262 1262 1262 1262 1262 1262 ...
$ site : Factor w/ 272 levels "S001","S002",..: 174 174 174 174 174 174 174 174 174 174 ...
$ year : Factor w/ 33 levels "1989","1990",..: 32 32 32 32 32 32 32 32 32 32 ...
$ week : Factor w/ 21 levels "1","2","3","4",..: 5 5 5 5 5 5 5 5 5 5 ...
Follow-up tests (from comments)
Fixed effect tests
1) Limiting to the 5 most abundant species, I get convergence warning 10.
# Model: count ~ species*year, ziformula = ~species
Warning message:
In fitTMB(TMBStruc) :
Model convergence problem; iteration limit reached without convergence (10). See vignette('troubleshooting')
2) Limiting to top 10 most abundant species, I get convergence warning 9.
# Model: count ~ species*year, ziformula = ~species
Warning message:
In fitTMB(TMBStruc) :
Model convergence problem; function evaluation limit reached without convergence (9). See vignette('troubleshooting')
3) Limiting to the top 2 most abundant species: The model appears to run without issue if the ziformula is just ~1 (count ~ species*year, ziformula = ~1). But, if I extend it to include the top 5 or the 10 most abundant species, it gives me convergence warning (9), and if I include all 40 species, it crashes R entirely.
4) Using just data from the top 2 most abundant species: if I include the week term, too (because species migrate over the 21 weeks), then I get a warning about the Hessian and also convergence warning (9):
# Model: count ~ species*week*year, ziformula = ~ 1
Warning messages:
1: In fitTMB(TMBStruc) :
Model convergence problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
2: In fitTMB(TMBStruc) :
Model convergence problem; function evaluation limit reached without convergence (9). See vignette('troubleshooting')
Random effect tests
1) Contrarily, if I use random effects (see model below), then I can include species in the ziformula as a random effect and the model runs without errors.
count ~ (species|year), ziformula = ~ (1|species)
So, it seems like random effects might be the only option? However, I’m not quite sure which random effects coding is justifiable for species-by-year. It seems to me that species should only be crossed with year, but besides (species|year), I don’t see any other way to produce separate species-by-year estimates without using a nested structure, which does not reflect reality given my understanding of what nested means (vs crossed). Is that the case?
2) Another note: Limiting to the top 10 species, if I use: count ~ species + (species|year), then the model allows a fixed species effect for zero-inflation: ziformula: ~species. (I'm currently running this for all 40 species, but it's taking a while.)
Setup:
I'm testing if the association between pairs of individuals for a trait (BMI) changes over time. I have repeated measures, where each individual in a pair gives BMI data at 7 points in time. Below is a simplified data frame in long format with Pair ID (the identifier given to each pair of individuals), BMI measurements for both individuals at each point in time (BMI_1 and BMI_2), and a time variable with seven intervals, coded as continuous.
Pair_ID
BMI_1
BMI_2
Time
1
25
22
1
1
23
24
2
1
22
31
3
1
20
27
4
1
30
26
5
1
31
21
6
1
19
18
7
2
21
17
1
2
22
27
2
2
24
22
3
2
25
20
4
First, I'm mainly interested in testing the within-pair association (the regression coefficient of BMI_2, below) and whether it changes over time (the interaction between BMI_2 and Time). I'd like to exclude any between-pair effects, so that I'm only testing associated over time within pairs.
I was planning on fitting a linear mixed model of the form:
lmer(BMI_1 ~ BMI_2 * Time + (BMI_2 | Pair_ID), Data)
I understand the parameters of the model (e.g., random slopes/intercepts), and that the BMI_2 * Time interaction tests whether the relationship between BMI_1 and BMI_2 is moderated by time.
However, I'm unsure how to identify the (mean) within-pair regression coefficients, and whether my approach is even suitable for this.
Second, I'm interested in understanding whether there is variation between pairs in the BMI_2 * Time interaction (i.e., the variance in slopes among pairs) - for example, does the associated between BMI_1 and BMI_2 increase over time in some pairs but not others?
For this, I was considering fitting a model like this:
lmer(BMI_1 ~ BMI_2 * Time + (BMI_2 : Time | Pair_ID), Data)
and then looking at the variance in the BMI_2 : Time random effect. As I understand it, large variance would imply that this interaction effect varied a lot between pairs.
Any help on these questions (especially the first question) would be greatly appreciated.
P.s., sorry if the question is poorly formatted. It's my first attempt.
Answering for completeness. #benimwolfspelz's comment is spot on. This is known as "contextual effects" in some areas of applied work. The idea is to split the variable into between and within components by mean-centering each group and fitting the mean-centred variable (which will estimate the within component) and the group means (which will estimate the between component).
Could someone help me to determine the correct random variable structure in my binomial GLMM in lme4?
I will first try to explain my data as best as I can. I have binomial data of seedlings that were eaten (1) or not eaten (0), together with data of vegetation cover. I try to figure out if there is a relationship between vegetation cover and the probability of a tree being eaten, as the other vegetation is a food source that could attract herbivores to a certain forest patch.
The data is collected in ~90 plots scattered over a National Park for 9 years now. Some were measured all years, some were measured only a few years (destroyed/newly added plots). The original datasets is split in 2 (deciduous vs coniferous), both containing ~55.000 entries. Per plot about 100 saplings were measured every time, so the two separate datasets probably contain about 50 trees per plot (though this will not always be the case, since the decid:conif ratio is not always equal). Each plot consists of 4 subplots.
I am aware that there might be spatial autocorrelation due to plot placement, but we will not correct for this, yet.
Every year the vegetation is surveyed in the same period. Vegetation cover is estimated at plot-level, individual trees (binary) are measured at a subplot-level.
All trees are measured, so the amount of responses per subplot will differ between subplots and years, as the forest naturally regenerates.
Unfortunately, I cannot share my original data, but I tried to create an example that captures the essentials:
#set seed for whole procedure
addTaskCallback(function(...) {set.seed(453);TRUE})
# Generate vector containing individual vegetation covers (in %)
cover1vec <- c(sample(0:100,10, replace = TRUE)) #the ',number' is amount of covers generated
# Create dataset
DT <- data.frame(
eaten = sample(c(0,1), 80, replace = TRUE),
plot = as.factor(rep(c(1:5), each = 16)),
subplot = as.factor(rep(c(1:4), each = 2)),
year = as.factor(rep(c(2012,2013), each = 8)),
cover1 = rep(cover1vec, each = 8)
)
Which will generate this dataset:
>DT
eaten plot subplot year cover1
1 0 1 1 2012 4
2 0 1 1 2012 4
3 1 1 2 2012 4
4 1 1 2 2012 4
5 0 1 3 2012 4
6 1 1 3 2012 4
7 0 1 4 2012 4
8 1 1 4 2012 4
9 1 1 1 2013 77
10 0 1 1 2013 77
11 0 1 2 2013 77
12 1 1 2 2013 77
13 1 1 3 2013 77
14 0 1 3 2013 77
15 1 1 4 2013 77
16 0 1 4 2013 77
17 0 2 1 2012 46
18 0 2 1 2012 46
19 0 2 2 2012 46
20 1 2 2 2012 46
....etc....
80 0 5 4 2013 82
Note1: to clarify again, in this example the number of responses is the same for every subplot:year combination, making the data balanced, which is not the case in the original dataset.
Note2: this example can not be run in a GLMM, as I get a singularity warning and all my random effect measurements are zero. Apparently my example is not appropriate to actually use (because using sample() caused the 0 and 1 to be in too even amounts to have large enough effects?).
As you can see from the example, cover data is the same for every plot:year combination.
Plots are measured multiple years (only 2012 and 2013 in the example), so there are repeated measures.
Additionally, a year effect is likely, given the fact that we have e.g. drier/wetter years.
First I thought about the following model structure:
library(lme4)
mod1 <- glmer(eaten ~ cover1 + (1 | year) + (1 | plot), data = DT, family = binomial)
summary(mod1)
Where (1 | year) should correct for differences between years and (1 | plot) should correct for the repeated measures.
But then I started thinking: all trees measured in plot 1, during year 2012 will be more similar to each other than when they are compared with (partially the same) trees from plot 1, during year 2013.
So, I doubt that this random model structure will correct for this within plot temporal effect.
So my best guess is to add another random variable, where this "interaction" is accounted for.
I know of two ways to possibly achieve this:
Method 1.
Adding the random variable " + (1 | year:plot)"
Method 2.
Adding the random variable " + (1 | year/plot)"
From what other people told me, I still do not know the difference between the two.
I saw that Method 2 added an extra random variable (year.1) compared to Method 1, but I do not know how to interpret that extra random variable.
As an example, I added the Random effects summary using Method 2 (zeros due to singularity issues with my example data):
Random effects:
Groups Name Variance Std.Dev.
plot.year (Intercept) 0 0
plot (Intercept) 0 0
year (Intercept) 0 0
year.1 (Intercept) 0 0
Number of obs: 80, groups: plot:year, 10; plot, 5; year, 2
Can someone explain me the actual difference between Method 1 and Method 2?
I am trying to understand what is happening, but cannot grasp it.
I already tried to get advice from a colleague and he mentioned that it is likely more appropriate to use cbind(success, failure) per plot:year combination.
Via this site I found that cbind is used in binomial models when Ntrails > 1, which I think is indeed the case given our sampling procedure.
I wonder, if cbind is already used on a plot:year combination, whether I need to add a plot:year random variable?
When using cbind, the example data would look like this:
>DT3
plot year cover1 Eaten_suc Eaten_fail
8 1 2012 4 4 4
16 1 2013 77 4 4
24 2 2012 46 2 6
32 2 2013 26 6 2
40 3 2012 91 2 6
48 3 2013 40 3 5
56 4 2012 61 5 3
64 4 2013 19 2 6
72 5 2012 19 5 3
80 5 2013 82 2 6
What would be the correct random model structure and why?
I was thinking about:
Possibility A
mod4 <- glmer(cbind(Eaten_suc, Eaten_fail) ~ cover1 + (1 | year) + (1 | plot),
data = DT3, family = binomial)
Possibility B
mod5 <- glmer(cbind(Eaten_suc, Eaten_fail) ~ cover1 + (1 | year) + (1 | plot) + (1 | year:plot),
data = DT3, family = binomial)
But doesn't cbind(success, failure) already correct for the year:plot dependence?
Possibility C
mod6 <- glmer(cbind(Eaten_suc, Eaten_fail) ~ cover1 + (1 | year) + (1 | plot) + (1 | year/plot),
data = DT3, family = binomial)
As I do not yet understand the difference between year:plot and year/plot
Thus: Is it indeed more appropriate to use the cbind-method than the raw binary data? And what random model structure would be necessary to prevent pseudoreplication and other dependencies?
Thank you in advance for your time and input!
EDIT 7/12/20: I added some extra information about the original data
You are asking quite a few questions in your question. I'll try to cover them all, but I do suggest reading the documentation and vignette from lme4 and the glmmFAQ page for more information. Also I'd highly recommend searching for these topics on google scholar, as they are fairly well covered.
I'll start somewhere simple
Note 2 (why is my model singular?)
Your model is highly singular, because the way you are simulating your data does not indicate any dependency between the data itself. If you wanted to simulate a binomial model you would use g(eta) = X %*% beta to simulate your linear predictor and thus the probability for success. One can then use this probability for simulating the your binary outcome. This would thus be a 2 step process, first using some known X or randomly simulated X given some prior distribution of our choosing. In the second step we would then use rbinom to simulate binary outcome while keeping it dependent on our predictor X.
In your example you are simulating independent X and a y where the probability is independent of X as well. Thus, when we look at the outcome y the probability of success is equal to p=c for all subgroup for some constant c.
Can someone explain me the actual difference between Method 1 and Method 2? ((1| year:plot) vs (1|year/plot))
This is explained in the package vignette fitting linear mixed effects models with lme4 in the table on page 7.
(1|year/plot) indicates that we have 2 mixed intercept effects, year and plot and plot is nested within year.
(1|year:plot) indicates a single mixed intercept effect, plot nested within year. Eg. we do not include the main effect of year. It would be somewhat similar to having a model without intercept (although less drastic, and interpretation is not destroyed).
It is more common to see the first rather than the second, but we could write the first as a function of the second (1|year) + (1|year:plot).
Thus: Is it indeed more appropriate to use the cbind-method than the raw binary data?
cbind in a formula is used for binomial data (or multivariate analysis), while for binary data we use the raw vector or 0/1 indicating success/failure, eg. aggregate binary data (similar to how we'd use glm). If you are uninterested in the random/fixed effect of subplot, you might be able to aggregate your data across plots, and then it would likely make sense. Otherwise stay with you 0/1 outcome vector indicating either success or failures.
What would be the correct random model structure and why?
This is a topic that is extremely hard to give a definitive answer to, and one that is still actively researched. Depending on your statistical paradigm opinions differ greatly.
Method 1: The classic approach
Classic mixed modelling is based upon knowledge of the data you are working with. In general there are several "rules of thumb" for choosing these parameters. I've gone through a few in my answer here. In general if you are "not interested" in the systematic effect and it can be thought of as a random sample of some population, then it could be a random effect. If it is the population, eg. samples do not change if the process is repeated, then it likely shouldn't.
This approach often yields "decent" choices for those who are new to mixed effect models, but is highly criticized by authors who tend towards methods similar to those we'd use in non-mixed models (eg. visualizing to base our choice and testing for significance).
Method 2: Using visualization
If you are able to split your data into independent subgroups and keeping the fixed effect structure a reasonable approach for checking potential random effects is the estimate marginal models (eg. using glm) across these subgroups and seeing if the fixed effects are "normally distributed" between these observations. The function lmList (in lme4) is designed for this specific approach. In linear models we would indeed expect these to be normally distributed, and thus we can get an indication whether a specific grouping "might" be a valid random effect structure. I believe the same is approximately true in the case of generalized linear models, but I lack references. I know that Ben Bolker have advocated for this approach in a prior article of his (the first reference below) that I used during my thesis. However this is only a valid approach for strictly separable data, and the implementation is not robust in the case where factor levels are not shared across all groups.
So in short: If you have the right data, this approach is simple, fast and seemingly highly reliable.
Method 3: Fitting maximal/minimal models and decreasing/expanding model based on AIC or AICc (or p-value tests or alternative metrics)
Finally an alternative to use a "step-wise"-like procedure. There are advocates of both starting with maximal and minimal models (I'm certain at least one of my references below talk about problems with both, otherwise check glmmFAQ) and then testing your random effects for their validity. Just like classic regression this is somewhat of a double-edged sword. The reason is both extremely simple to understand and amazingly complex to comprehend.
For this method to be successful you'd have to perform cross-validation or out-of-sample validation to avoid selection bias just like standard models, but unlike standard models sampling becomes complicated because:
The fixed effects are conditional on the random structure.
You will need your training and testing samples to be independent
As this is dependent on your random structure, and this is chosen in a step-wise approach it is hard to avoid information leakage in some of your models.
The only certain way to avoid problems here is to define the space
that you will be testing and selecting samples based on the most
restrictive model definition.
Next we also have problems with choice of metrics for evaluation. If one is interested in the random effects it makes sense to use AICc (AIC estimate of the conditional model) while for fixed effects it might make more sense to optimize AIC (AIC estimate of the marginal model). I'd suggest checking references to AIC and AICc on glmmFAQ, and be wary since the large-sample results for these may be uncertain outside a very reestrictive set of mixed models (namely "enough independent samples over random effects").
Another approach here is to use p-values instead of some metric for the procedure. But one should likely be even more wary of test on random effects. Even using a Bayesian approach or bootstrapping with incredibly high number of resamples sometimes these are just not very good. Again we need "enough independent samples over random effects" to ensure the accuracy.
The DHARMA provides some very interesting testing methods for mixed effects that might be better suited. While I was working in the area the author was still (seemingly) developing an article documenting the validity of their chosen method. Even if one does not use it for initial selection I can only recommend checking it out and deciding upon whether one believes in their methods. It is by far the most simple approach for a visual test with simple interpretation (eg. almost no prior knowledge is needed to interpret the plots).
A final note on this method would thus be: It is indeed an approach, but one I would personally not recommend. It requires either extreme care or the author accepting ignorance of model assumptions.
Conclusion
Mixed effect parameter selection is something that is difficult. My experience tells me that mostly a combination of method 1 and 2 are used, while method 3 seems to be used mostly by newer authors and these tend to ignore either out-of-sample error (measure model metrics based on the data used for training), ignore independence of samples problems when fitting random effects or restrict themselves to only using this method for testing fixed effect parameters. All 3 do however have some validity. I myself tend to be in the first group, and base my decision upon my "experience" within the field, rule-of-thumbs and the restrictions of my data.
Your specific problem.
Given your specific problem I would assume a mixed effect structure of (1|year/plot/subplot) would be the correct structure. If you add autoregressive (time-spatial) effects likely year disappears. The reason for this structure is that in geo-analysis and analysis of land plots the classic approach is to include an effect for each plot. If each plot can then further be indexed into subplot it is natural to think of "subplot" to be nested in "plot". Assuming you do not model autoregressive effects I would think of time as random for reasons that you already stated. Some years we'll have more dry and hotter weather than others. As the plots measured will have to be present in a given year, these would be nested in year.
This is what I'd call the maximal model and it might not be feasible depending on your amount of data. In this case I would try using (1|time) + (1|plot/subplot). If both are feasible I would compare these models, either using bootstrapping methods or approximate LRT tests.
Note: It seems not unlikely that (1|time/plot/subplot) would result in "individual level effects". Eg 1 random effect per row in your data. For reasons that I have long since forgotten (but once read) it is not plausible to have individual (also called subject-level) effects in binary mixed models. In this case It might also make sense to use the alternative approach or test whether your model assumptions are kept when withholding subplot from your random effects.
Below I've added some useful references, some of which are directly relevant to the question. In addition check out the glmmFAQ site by Ben Bolker and more.
References
Bolker, B. et al. (2009). „Generalized linear mixed models: a practical guide for ecology and evolution“. In: Trends in ecology & evolution 24.3, p. 127–135.
Bolker, B. et al. (2011). „GLMMs in action: gene-by-environment interaction in total fruit production of wild populations of Arabidopsis thaliana“. In: Revised version, part 1 1, p. 127–135.
Eager, C. og J. Roy (2017). „Mixed effects models are sometimes terrible“. In: arXiv preprint arXiv:1701.04858. url: https://arxiv.org/abs/1701.04858 (last seen 19.09.2019).
Feng, Cindy et al. (2017). „Randomized quantile residuals: an omnibus model diagnostic tool with unified reference distribution“. In: arXiv preprint arXiv:1708.08527. (last seen 19.09.2019).
Gelman, A. og Jennifer Hill (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Hartig, F. (2019). DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models. R package version 0.2.4. url: http://florianhartig.github.io/DHARMa/ (last seen 19.09.2019).
Lee, Y. og J. A. Nelder (2004). „Conditional and Marginal Models: Another View“. In: Statistical Science 19.2, p. 219–238.
doi: 10.1214/088342304000000305. url: https://doi.org/10.1214/088342304000000305
Lin, D. Y. et al. (2002). „Model-checking techniques based on cumulative residuals“. In: Biometrics 58.1, p. 1–12. (last seen 19.09.2019).
Lin, X. (1997). „Variance Component Testing in Generalised Linear Models with Random Effects“. In: Biometrika 84.2, p. 309–326. issn: 00063444. url: http://www.jstor.org/stable/2337459
(last seen 19.09.2019).
Stiratelli, R. et al. (1984). „Random-effects models for serial observations with binary response“. In:
Biometrics, p. 961–971.
I have a question concerning multi level regression models in R, specifically how to add predictors for my level 2 "measure".
Please consider the following example (this is not a real dataset, so the values might not make much sense in reality):
date id count bmi poll
2012-08-05 1 3 20.5 1500
2012-08-06 1 2 20.5 1400
2012-08-05 2 0 23 1500
2012-08-06 2 3 23 1400
The data contains
different persons ("id"...so it's two persons)
the body mass index of each person ("bmi", so it doesn't vary within an id)
the number of heart problems each person has on a specific day ("count). So person 1 had three problems on August the 5th, whereas person 2 had no difficulties/problems on that day
the amount of pollutants (like Ozon or sulfit dioxide) which have been measured on that given day
My general research question is, if the amount of pollutants effects the numer of heart problems in the population.
In a first step, this could be a simple linear regression:
lm(count ~ poll)
However, my data for each day is so to say clustered within persons. I have two measures from person 1 and two measures from person 2.
So my basic idea was to set up a multilevel model with persons (id) as my level 2 variable.
I used the nlme package for this analysis:
lme(fixed=count ~ poll, random = ~poll|id, ...)
No problems so far.
However, the true influence on level 2 might not only come from the fact that I have different persons. Rather it would be much more likely that the effect WITHIN a person might come from his or her bmi (and many other person related variables, like age, amount of smoking and so on).
To make a longstory short:
How can I specify such level two predictors in the lme function?
Or in other words: How can I setup a model, where the relationship between heart problems and pollution is different/clustered/moderated by the body mass index of a person (and as I said maybe additionally by this person's amount of smoking or age)
Unfortunately, I don't have a clue, how to tell R, what I want. I know oif other software (one of them called HLM), which is capable of doing waht I want, but I'm quite sure that R can this as well...
So, many thanks for any help!
deschen
Short answer: you do not have to, as long as you correctly specify random effects. The lme function automatically detects which variables are level 1 or 2. Consider this example using Oxboys where each subject was measured 9 times. For the time being, let me use lmer in the lme4 package.
library(nlme)
library(dplyr)
library(lme4)
library(lmerTest)
Oxboys %>% #1
filter(as.numeric(Subject)<25) %>% #2
mutate(Group=rep(LETTERS[1:3], each=72)) %>% #3
lmer(height ~ Occasion*Group + (1|Subject), data=.) %>% #4
anova() #5
Here I am picking 24 subjects (#2) and arranging them into 3 groups (#3) to make this data balanced. Now the design of this study is a split-plot design with a repeated-measures factor (Occasion) with q=9 levels and a between-subject factor (Group) with p=3 levels. Each group has n=8 subjects. Occasion is a level-1 variable while Group is level 2.
In #4, I did not specify which variable is level 1 or 2, but lmer gives you correct output. How do I know it is correct? Let us check the multi-level model's degrees of freedom for the fixed effects. If your data is balanced, the Kenward–Roger approximation used in the lmerTest will give you exact dfs and F/t-ratios according to this article. That is, in this example dfs for the test of Group, Occasion, and their interaction should be p-1=2, q-1=8, and (p-1)*(q-1)=16, respectively. The df for the Subject error term is (n-1)p = 21 and the df for the Subject:Occasion error term is p(n-1)(q-1)=168. In fact, these are the "exact" values we get from the anova output (#5).
I do not know what algorithm lme uses for approximating dfs, but lme does give you the same dfs. So I am assuming that it is accurate.
I'm having trouble trying to figure out the following: I am running Random Forest for classification of habitat use and have GPS data from 17 animals. My data frame depicts different habitat variables such as aspect and canopy cover at each used animal location and each unused, random location. Each used location is also identified by the ID number of the animal ( this column is called "lynx"). A column called "usvsa" codes used locations as 1 and unused locations as 0. Here's the top of my spatial points data frame called sdata3:
lynx usvsa aspect canopy_cover clearcut_area cti deciduous dist_draw dist_ridge
311 1 252.3302 55.3704 0 7.311823 0 90.0000 484.66483
311 1 263.1394 55.1528 0 6.857203 0 324.4996 305.94116
311 1 249.6992 72.9272 0 6.612025 0 364.9658 212.13203
311 1 194.4459 50.4428 0 6.330615 0 108.1665 67.08204
Ok. So, I'd like to use Jackknifing to run Random Forest 17 times (since I have 17 individuals), leaving one animal out each run. The idea is to compare the results of each random forest run to make sure no one animal is having a disproportionately large effect on the model results. I've been reading about package "bootstrap" and the jackknife function: jackknife(x, theta, ...)
I get that I need to write a function for theta but I can't figure out how to put it all together so that each run of Random Forest leaves one animal out. Here is my Random Forest Model: randomForest(y ~ ., data=sdata3, ntree=b, importance=TRUE,norm.votes=TRUE, proximity=TRUE) I'd like to compare the importance values and oob error of each run.
Any tips would be appreciated!!