I am very new to working with GLM. I have a dataset with categorical (as factors) and numerical predictor variables and the response variable is count data wiht a poisson distribution. These I put in a glm:
glm2<- glm(formula = count ~ Salinity + Period + Intensity + Depth + Temp + Treatment, data = dfglm, family = "poisson")
Treatment(1.1 - 3.6) and Period (morning/midday) are factors.
The output looks like this:
I already see multiple suprising things in this output (very big difference between the null-deviance and residual deviance, treatment 1.1 not showing, period morning and midday not shown as separate levels, very high standard errors) but I will continue for now.
For the backward selection I used this code:
backward<-step(glm2,direction="backward",trace=0)
summary(backward)
I got exactly the same output as given above. Also when checking backward$coefficients, all coefficients remained.
Lastly I tried this:
If anyone could give me advice/an interpretation of this output and how to make a better model with a working backward selection, it is greatly appreciated!
Related
I am attempting to model binary species traits, where presence is represented by 1 and absence by 0, as a function of some sampling variables. To accomplish this, I have constructed a brms model and added a phylogenetic structure to it. Here is the model I used:
model <- brms::brm(male_head | trials(1 + 0) ~
PC1 + PC2 + PC3 +
(1|gr(phylo, cov = covariance_matrix)),
data = data,
family = binomial(),
prior = prior,
data2 = list(covariance_matrix = covariance_matrix))
Each line of my df represents one observation with a binary outcome.
Initially, I was unsure about which arguments to use in the trials() function. Since my species are non-repeated and some have the traits I'm modeling while others do not, I thought that trials(1 + 0) might be appropriate. I recall seeing a vignette that suggested this, but I can't find it now. Is this syntax correct?
Furthermore, for some reason I'm unaware, the model is producing one estimate value for each line of my predictors. As my df has 362 lines, the model summary displays a lengthy list of 362 estimate values. I would prefer to have one estimate value for each sampling variable instead. Although I have managed to achieve this by making the treatment effect a random effect (i.e., (1|PC1) + (1|PC2) + (1|PC3)), I don't think this is the appropriate approach. I also tried bernoulli() but no success either. Do you have any suggestions for how I can address this issue?
EDIT:
For some reason the values of my sampling variables/principal components were being read as factors. The second part of this question was solved.
I am trying to create a GLMM in R. I want to find out how the emergence time of bats depends on different factors. Here I take the time difference between the departure of the respective bat and the sunset of the day as dependent variable (metric). As fixed factors I would like to include different weather data (metric) as well as the reproductive state (categorical) of the bats. Additionally, there is the transponder number (individual identification code) as a random factor to exclude inter-individual differences between the bats.
I first worked in R with a linear mixed model (package lme4), but the QQ plot of the residuals deviates very strongly from the normal distribution. Also a histogram of the data rather indicates a gamma distribution. As a result, I implemented a GLMM with a gamma distribution. Here is an example with one weather parameter:
model <- glmer(formula = difference_in_min ~ repro + precipitation + (1+repro|transponder number), data = trip, control=ctrl, family=gamma(link = log))
However, since there was no change in the QQ plot this way, I looked at the residual diagnostics of the DHARMa package. But the distribution assumption still doesn't seem to be correct, because the data in the QQ plot deviates very much here, too.
Residual diagnostics from DHARMa
But if the data also do not correspond to a gamma distribution, what alternative is there? Or maybe the problem lies somewhere else entirely.
Does anyone have an idea where the error might lie?
But if the data also do not correspond to a gamma distribution, what alternative is there?
One alternative is called the lognormal distribution (https://en.wikipedia.org/wiki/Log-normal_distribution)
Gaussian (or normal) distributions are typically used for data that are normally distributed around zero, which sounds like you do not have. But the lognormal distribution does not have the same requirements. Following your previous code, you would fit it like this:
model <- glmer(formula = log(difference_in_min) ~ repro + precipitation + (1+repro|transponder number), data = trip, control=ctrl, family=gaussian(link = identity))
or instead of glmer you can just call lmer directly where you don't need to specify the distribution (which it may tell you to do in a warning message anyway:
model <- lmer(formula = log(difference_in_min) ~ repro + precipitation + (1+repro|transponder number), data = trip, control=ctrl)
I want to estimate a regression for a variable, LWAGE (log wage), against EXP (years of work experience). The data that I have has participants tracked across 7 years, so each year their number of years of work experience increases by 1.
When I do the regression for
πΏππ΄πΊπΈπ = π½0 + π½1πΈπ·π + π’π
I used
reg1 <- lm(LWAGE~EXP, data=df)
Now I'm trying to do the following regression:
πΏππ΄πΊπΈππ‘ = π½0 + π½1πΈππππ‘ + π’i.
But I'm not sure how to include my the time based component into my regression. I searched around but couldn't find anything relevant.
Are you attempting to include time-fixed effects in your model or an interaction between your variable EXP and time (calling this TIME for this demonstration)?
For time fixed effects using lm() you can just include time as a variable in your model. Time should be a factor.
reg2 <- lm(LWAGE~EXP + TIME, data = df)
As an interaction between EXP and TIME it would be
reg3 <- lm(LWAGE~EXP*TIME, data = df)
Based on your description it sounds like you might be looking for the interaction. I.e. How does the effect of experience on log of wages vary by time?
You can also take a look at the plm package for working with panel data.
https://cran.r-project.org/web/packages/plm/vignettes/plmPackage.html
In the afex package we can find this example of ANOVA analysis:
data(obk.long, package = "afex")
# estimate mixed ANOVA on the full design:
# can be written in any of these ways:
aov_car(value ~ treatment * gender + Error(id/(phase*hour)), data = obk.long,
observed = "gender")
aov_4(value ~ treatment * gender + (phase*hour|id), data = obk.long,
observed = "gender")
aov_ez("id", "value", obk.long, between = c("treatment", "gender"),
within = c("phase", "hour"), observed = "gender")
My question is, How can I write the same model in lme4?
In particular, I don't know how to include the "observed" term?
If I just write
lmer(value ~ treatment * gender + (phase*hour|id), data = obk.long,
observed = "gender")
I get an error telling that observed is not a valid option.
Furthermore, if I just remove the observed option lmer produces the error:
Error: number of observations (=240) <= number of random effects (=240) for term (phase * hour | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable.
Where in the lmer syntax do I specify the "between" or "within" variable?. As far as I know you just write the dependent variable on the left side and all other variables on the right side, and the error term as (1|id).
The package "car" uses the idata for the intra-subject variable.
I might not know enough about classical ANOVA theory to answer this question completely, but I'll take a crack. First, a couple of points:
the observed argument appears only to be relevant for the computation of effect size.
observed: βcharacterβ vector indicating which of the variables are
observed (i.e, measured) as compared to experimentally
manipulated. The default effect size reported (generalized
eta-squared) requires correct specification of the obsered [sic]
(in contrast to manipulated) variables.
... so I think you'd be safe leaving it out.
if you want to override the error you can use
control=lmerControl(check.nobs.vs.nRE="ignore")
... but this probably isn't the right way forward.
I think but am not sure that this is the right way:
m1 <- lmer(value ~ treatment * gender + (1|id/phase:hour), data = obk.long,
control=lmerControl(check.nobs.vs.nRE="ignore",
check.nobs.vs.nlev="ignore"),
contrasts=list(treatment=contr.sum,gender=contr.sum))
This specifies that the interaction of phase and hour varies within id. The residual variance and (phase by hour within id) variance are confounded (which is why we need the overriding lmerControl() specification), so don't trust those particular variance estimates. However, the main effects of treatment and gender should be handled just the same. If you load lmerTest instead of lmer and run summary(m1) or anova(m1) it gives you the same degrees of freedom (10) for the fixed (gender and treatment) effects that are computed by afex.
lme gives comparable answers, but needs to have the phase-by-hour interaction constructed beforehand:
library(nlme)
obk.long$ph <- with(obk.long,interaction(phase,hour))
m2 <- lme(value ~ treatment * gender,
random=~1|id/ph, data = obk.long,
contrasts=list(treatment=contr.sum,gender=contr.sum))
anova(m2,type="marginal")
I don't know how to reconstruct afex's tests of the random effects.
As Ben Bolker correctly says, simply leave observed out.
Furthermore, I would not recommend to do what you want to do. Using a mixed model for a data set without replications within each cell of the design per participant is somewhat questionable as it is not really clear how to specify the random effects structure. Importantly, the Barr et al. maxim of "keep it maximal" does not work here as you realized. The problem is that the model is overparametrized (hence the error from lmer).
I recommend using the ANOVA. More discussion on exactly this question can be found on a crossvalidated thread where Ben and me discussed this more thoroughly.
I am currently working through Andy Field's book, Discovering Statistics Using R. Chapter 14 is on Mixed Modelling and he uses the lme function from the nlme package.
The model he creates, using speed dating data, is such:
speedDateModel <- lme(dateRating ~ looks + personality +
gender + looks:gender + personality:gender +
looks:personality,
random = ~1|participant/looks/personality)
I tried to recreate a similar model using the lmer function from the lme4 package; however, my results are different. I thought I had the proper syntax, but maybe not?
speedDateModel.2 <- lmer(dateRating ~ looks + personality + gender +
looks:gender + personality:gender +
(1|participant) + (1|looks) + (1|personality),
data = speedData, REML = FALSE)
Also, when I run the coefficients of these models I notice that it only produces random intercepts for each participant. I was trying to then create a model that produces both random intercepts and slopes. I can't seem to get the syntax correct for either function to do this. Any help would be greatly appreciated.
The only difference between the lme and the corresponding lmer formula should be that the random and fixed components are aggregated into a single formula:
dateRating ~ looks + personality +
gender + looks:gender + personality:gender +
looks:personality+ (1|participant/looks/personality)
using (1|participant) + (1|looks) + (1|personality) is only equivalent if looks and personality have unique values at each nested level.
It's not clear what continuous variable you want to define your slopes: if you have a continuous variable x and groups g, then (x|g) or equivalently (1+x|g) will give you a random-slopes model (x should also be included in the fixed-effects part of the model, i.e. the full formula should be y~x+(x|g) ...)
update: I got the data, or rather a script file that allows one to reconstruct the data, from here. Field makes a common mistake in his book, which I have made several times in the past: since there is only a single observation in the data set for each participant/looks/personality combination, the three-way interaction has one level per observation. In a linear mixed model, this means the variance at the lowest level of nesting will be confounded with the residual variance.
You can see this in two ways:
lme appears to fit the model just fine, but if you try to calculate confidence intervals via intervals(), you get
intervals(speedDateModel)
## Error in intervals.lme(speedDateModel) :
## cannot get confidence intervals on var-cov components:
## Non-positive definite approximate variance-covariance
If you try this with lmer you get:
## Error: number of levels of each grouping factor
## must be < number of observations
In both cases, this is a clue that something's wrong. (You can overcome this in lmer if you really want to: see ?lmerControl.)
If we leave out the lowest grouping level, everything works fine:
sd2 <- lmer(dateRating ~ looks + personality +
gender + looks:gender + personality:gender +
looks:personality+
(1|participant/looks),
data=speedData)
Compare lmer and lme fixed effects:
all.equal(fixef(sd2),fixef(speedDateModel)) ## TRUE
The starling example here gives another example and further explanation of this issue.