I'm analyzing some longitudinal data using lme4 package (lmer function) with 3 Levels: measurement points nested in individuals nested in households. I'm interested in linear and non-linear change curves surrounding a specific life event. My model has many time predictors (indicating linear change before and after the event occurs and indicating non-linear change (i.e., squared time variables) before and after the event occurs). Additionally, I have several Level-2 predictors that do not vary with time (i.e., personality traits) and some control variables (e.g., age, gender). So far I did not include any random slopes or cross-level interactions.
This is my model code:
model.RI <- lmer(outcome ~ time + female_c + age_c + age_c2 + preLin + preLin.sq + postLin + postLin.sq + per1.c + per2.c + per3.c + per4.c + per5.c + (1 | ID) + (1 | House))
outcome = my dependent variable
time = year 1, year 2, year 3 ... (until year 9); this variable symbolizes something like a testing effect
female_c = gender centered
age_c = age centered
age_c2 = age squared centered
preLin = time variable indicating time to the event (this variable is 0 after the event has occurred and is -1 e.g. one year ahead of the event, -2 two years ahead of the event etc.)
preLin.sq = squared values of preLin
postLin = time variable indicating time after the event (this variable is 0 before the event and increases after the event has occurred; e.g. is +1 one year after the event)
postLin.sq = squared values of postLin
per1.c until per5.c = personality traits on Level 2 (centered)
ID = indicating the individuum
House = indicating the household
I was wondering how I could plot the predicted values of this lmer model (e.g., using ggplot2?). I've plotted change curves using the method=gam in R. This is a rather data-driven method to inspect the data without pre-defining if the curve is linear or quadratic or whatever. I would now like to check whether my parametric lmer model is comparable to that data-driven gam-plot I already have. Do you have any advise how to do this?
I would be more than happy to get some help on this! Please also feel free to ask if I was not precise enough on my explanation of what I would like to do!
Thanks a lot!
Follow this link: This is how my gam-plot looks like and I hope to get something similar when plotting the predicted values of my lmer model!
You can use the ggpredict()-function from the ggeffects-package. If you want to plot predicted values of time (preLin), you would simply write:
ggpredict(model.RI, "preLin")
The function returns a data frame (see articles), which you can use in ggplot, but you can also directly plot the results:
ggpredict(model.RI, "preLin") %>% plot()
or
p <- ggpredict(model.RI, "preLin")
plot(p)
You could also use the sjPlot-package, however, for marginal effects / predicted values, the sjPlot::plot_model()-function internally just calls ggeffects::ggpredict(), so the results would basically be identical.
Another note to your model: if you have longitudinal data, you should also include your time-variable as random slope. I'm not sure how postLin acutally refers to preLin, but if preLin captures all your measurements, you should at least write your model like this:
model.RI <- lmer(
outcome ~ time + female_c + age_c + age_c2 + preLin + preLin.sq +
postLin + postLin.sq + per1.c + per2.c + per3.c + per4.c + per5.c +
(1 + preLin | ID) + (1 + preLin | House)
)
If you also assume a quadratic trend for each person (ID), you could even add the squared term as random slope.
As your figure example suggests using splines, you could also try this:
library(splines)
model.RI <- lmer(
outcome ~ time + female_c + age_c + age_c2 + bs(preLin)
postLin + postLin.sq + per1.c + per2.c + per3.c + per4.c + per5.c +
(1 + preLin | ID) + (1 + preLin | House)
)
p <- ggpredict(model.RI, "preLin")
plot(p)
Examples for splines are also demonstrated on the website I mentioned above.
Edit:
Another note is related to nesting: you're currently modelling a fully crossed or cross-classified model. If it's completely nested, the random parts would look like this:
... + (1 + preLin | House / ID)
(see also this small code-example).
Related
level 1 variable:
income - continuous
level 2 variable:
state's general whether: three leveled categorical variable: hot/moderate/cool
used effect coded, and generate two variables because it has three levels.
(weather_ef1, weather_ef2)
enrolled in university - binary : yes/no ( effect coded. yes = -1, no =1)
DV:
math score
grouping variable: household
model 1: (fixed slope)
Dv is predicted by income, enrollment, and the interaction between enrollment and income.
in this case,
lmer(y~ 1 + income + enrollment +income*enrollment+ (1|householdID), data=data)
lmer(y~ 1 + income + enrollment +income:enrollment+ (1|householdID), data=data)
: is it for interaction? or * is it for interaction?
further, do I have to do factor(enrollment)?
or is it okay because it is already effect coded?
model 2: (fixed slope)
DV is predicted by income, weather, and interaction between income and weather
lmer( y ~ 1 + income + weather_ef1 + weather_ef2 + weather_ef1*income
+ weather_ef2*income +(1|houshold_id), data)
lmer ( y ~ l + income + weather_ef1+ weather_ef2 + weather_ef1:income
+ weather_ef2:income + (1|houshold_id), data)
Still confusing * is right or: is right.
I think the effect code variables are already effect coded, so I don't have to
do use the factor(weather_ef1) things.
From the documentation (use ?formula):
The * operator denotes factor crossing: a*b interpreted as a+b+a:b.
In other words a*b adds the main effects of a and b and their interaction. So in your model when you use income*enrollment this is the same as income + enrollment +income:enrollment. The two versions you described for each model should give identical results. You could just have used:
lmer(y~ 1 + income*enrollment+ (1|householdID), data=data)
which also describes the same model.
If your variables are effect coded then you don't need to use factor but be careful about the interpretation of the effects.
I am running a gam model based on a large dataset with many variables. My response variable is the level of "recruitment" by a herd every fall/autumn. This is calculated by the fawn:female ratio every fall/autumn over a 60 year period.
My problem is that there are many years and study sites where only between 1 - 10 females are recorded. This means that the robustness of the ratio is not trustworthy. For example if one female and one fawn is seen, it has a recruitment of 100%, but if they see one more female, that drops by 50%!
I need to tell the model that years/study sites with smaller sample sizes should be weighted less than those with larger sample sizes as these smaller sample sizes are no doubt affecting the results.
Above is a table of the females observed every year and a histogram of the same.
My model is as follows:
gamFIN <- gam(Fw.FratioFall
~ s(year)
+ s(percentage_woody_coverage)
+ s(kmRoads.km2)
+ s(WELLS_ACTIVEinsideD)
+ s(d3)
+ s(WT_DEER_springsurveys)
+ s(BadlandsCoyote.1000_mi)
+ s(Average_mintemp_winter, BadlandsCoyote.1000_mi)
+ s(BadlandsCoyote.1000_mi, WELLS_ACTIVEinsideD)
+ s(BadlandsCoyote.1000_mi, d3)
+ s(YEAR, bs = "re") + s(StudyArea, bs = "re"), method = "REML", select = T, data = mydata)
How might I tell the model to weight my response variable by the sample sizes they are based on.
Do not model this as a ratio for your outcome. Instead model the fawn counts as your outcome and model the female counts via an offset() term using logged values on the RHS of the formula. You should be offsetting with the log of the fawn count. So the formula would look like this:
Fawns
~ s(year)
+ all_those_smooth_terms
+ offset( lnFemale_counts)
The gam models have an implicit log link which is the reason for the logging of the Female counts.
Edit (Gavin's correct. The default for gam is not a linear link):
gamFIN <- gam(FawnFall ~ s(year) + s(percentage_woody_coverage) + s(kmRoads.km2) +
s(WELLS_ACTIVEinsideD) + s(d3) + s(WT_DEER_springsurveys) +
s(BadlandsCoyote.1000_mi) + s(Average_mintemp_winter, BadlandsCoyote.1000_mi) +
s(BadlandsCoyote.1000_mi, WELLS_ACTIVEinsideD) + s(BadlandsCoyote.1000_mi, d3) +
s(YEAR, bs = "re") + s(StudyArea, bs = "re") + offset(FemaleFall),
family="poisson", method = "REML", select = T, data = mydata)
I'm trying to include time fixed effects (dummies for years generated with model.matrix) into a PPML regression in R.
Without time fixed effect the regression is:
require(gravity)
my_model <- PPML(y="v", dist="dist",
x=c("land","contig","comlang_ethno",
"smctry","tech","exrate"),
vce_robust=T, data=database)
I've tried to add command fe=c("year") within the PPML function but it doesn't work.
I'd appreciate any help on this.
I would comment on the previous answer but don't have enough reputation. The gravity model in your PPML command specifies v = dist × exp(land + contig + comlang_ethno + smctry + tech + exrate + TimeFE) = exp(log(dist) + land + contig + comlang_ethno + smctry + tech + exrate + TimeFE).
The formula inside of glm should have as its RHS the variables inside the exponential, because it represents the linear predictor produced by the link function (the Poisson default for which is natural log). So in sum, your command should be
glm(v ~ log(dist) + land + contig + comlang_ethno + smctry + tech + exrate + factor(year),
family='quasipoisson')
and in particular, you need to have distance in logs on the RHS (unlike the previous answer).
Just make sure that year is a factor, than you can just use the plain-and-simple glm-function as
glm(y ~ dist + year, family = "quasipoisson")
which gives you the results with year as dummies/fixed effects. The robust SE are then calculated with
lmtest::coeftest(EstimationResults.PPML, vcov=sandwich::vcovHC(model.PPML, "HC1"))
The PPML function does nothing more, it just isn't very flexible.
Alternatively to PPML and glm, you can also solve your problem using the function femlm (from package FENmlm) which deals with fixed-effect estimation for maximum likelihood models.
The two main advantages of function femlm are:
you can add as many fixed-effects as you want, and they are dealt with separately leading to computing times without comparison to glm (especially when fixed-effects contain many categories)
standard-errors can be clustered with intuitive commands
Here's an example regarding your problem (with just two variables and the year fixed-effects):
library(FENmlm)
# (default family is Poisson, 'pipe' separates variables from fixed-effects)
res = femlm(v ~ log(dist) + land | year, base)
summary(res, se = "cluster")
This code estimates the coefficients of variables log(dist) and land with year fixed-effects; then it displays the coefficients table with clustered standard-errors (w.r.t. year) for the two variables.
Going beyond your initial question, now assume you have a more complex case with three fixed-effects: country_i, country_j and year. You'd write:
res = femlm(v ~ log(dist) + land | country_i + country_j + year, base)
You can then easily play around with clustered standard-errors:
# Cluster w.r.t. country_i (default is first cluster encountered):
summary(res, se = "cluster")
summary(res, se = "cluster", cluster = "year") # cluster w.r.t. year cluster
# Two-way clustering:
summary(res, se = "twoway") # two-way clustering w.r.t. country_i & country_j
# two way clustering w.r.t. country_i & year:
summary(res, se = "twoway", cluster = c("country_i", "year"))
For more information on the package, the vignette can be found at https://cran.r-project.org/web/packages/FENmlm/vignettes/FENmlm.html.
First of all, I am relatively new in using R and haven't used lavaan (or growth models) before so please excuse my ignorance.
I am doing my thesis and analyzing the U.S. financial industry during the financial crisis of 2007. I therefore have individual banks and several variables for each bank across time (from 2007-2013), some are time-variant (such as ROA or capital adequacy) and some are time-invariant (such as size or age). Some variables are also time-variant but not multi-level since they apply to all firms (such as the average ROA of the U.S. financial industry).
Fist of all, can I use lavaan's growth curve model ("growth") in this instance? The example given on the tutorial is for either time-varying variables (c) that influence the outcome (DV) or time-invariant variables (x1 & x2) which influence the slope (s) and intercept (i). What about time varying variables that influence the slope and intercept? I couldn't find an example for this syntax.
Also, how do I specify the "groups" (i.e. different banks) in my analysis? It is actually possible to do a multi-level growth curve model in lavaan (or R for that matter)?
Last but not least, I could find how to import a multilevel dataset in R. My dataset is basically a 3-dimensional matrix (different variables for different firms across time) so how do I input that via SPSS (or notepad?)?
Any help is much appreciated, I am basically lost on how to implement this model and sincerely need some assistance...
Thank you all in advance for your time!
Harry
edit: Here is the sytanx that I have come with so far. DO you think it makes sense?
ETHthesismodel <- '
# intercept and slope with fixed coefficients
i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4
#regressions (independent variables that influence the slope & intercept)
i ~ high_constr_2007 + high_constr_2008 + ... + low_constr_2007 + low_constr_2008 + ... + ... diff_2013
s ~ high_constr_2007 + high_constr_2008 + ... + low_constr_2007 + low_constr_2008 + ... + ... diff_2013
# time-varying covariates (control variables)
t1 ~ size_2007 + cap_adeq_2007 + brand_2007 +... + acquisitions_2007
t2 ~ size_2008 + cap_adeq_2008 + brand_2008 + ... + acquisitions_2008
...
t7 ~ size_2013 + cap_adeq_2013 + brand_2013 + ... + acquisitions_2013
'
fit <- growth(ETHthesismodel, data = inputdata,
group = "bank")
summary(fit)
I have an experiment with 2 IVs, time (3 levels, t1, t2, t3, within subject), and correction type (3 levels, between subject). DV = attitude (continuous). The complete lmer model looks like this:
agreement ~ correction * time + (1 + time|subject) + (1 + correction + time|item)
How do I get simple effects from the overall model?
I would like to compare all three levels of correction at time point 3, but taking into account the individual participant scores at time point 1 (a baseline measure). This would be kind of like an ANCOVA on time point 3 with baseline scores from timepoint 1 as the continuous measure.
I can do this:
library(lsmeans)
ref_levs <- emmeans(mod2, "correction", by = "time", at = list(time = "t3"))
pairs(ref_levs)
But I cannot have the output of the comparisons that controls for the individual participant scores at t1.
Am I forced to subset the dataset to have what I need, fitting a model like this one?
agreement_t3 ~ correction + time_t1 + (1|subject) + (1 + correction|item)
Or there is a way in emmeans to obtain that without having to subset the dataset?
Though it appears that you want to treat the observation at time 1 as a covariate, I will nonetheless show a reasonable way of estimating change from baseline with the model shown in the OP.
First, set things up so we have time as the primary factor, and obtain contrasts that compare times 2 and 3 with time 1:
emm1 <- emmeans(mod2, ~ time | correction)
emm2 <- contrast(emm1, "trt.vs.ctrl1, name = "time.gap")
Now, time.gap is a new factor with just the two levels t2 - t1 and t3 - t1. So you can now compare those changes:
pairs(emm2, by = "time.gap")
It's possible to do this in fewer steps: contrast(emm1, interaction = c("trt.vs.ctrl1", "pairwise"), by = NULL); but I think the above is less confusing and easier to interpret.