I have fitted a few models using glmer from thelme4 package and did model selection with MuMIn::dredge() followed by model averaging. My response is frequency of occurrence of an animal in front of camera traps (continuous, number of photos per 100 hours of camera time); the predictors are minimum distances from a camera trap to landscape categories in meters, sometimes with an interaction with the day phase (day/night).
The response shows Gamma-distribution, but to make the model work I had to transform my response by adding 1, as the Gamma distribution can't handle non-positive data and quite a few of my data points were zeros as shown in this histogram:
Also, I had to scale the predictors, otherwise I got convergence warnings like
Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?
I did this with scale(..., center = TRUE).
My model formula looks like this:
mod <- glmer(Species_Frequency ~ scaled_Minimal_Distance1 +
scaled_Minimal_Distance2 +
(scaled_Minimal_Distance3 * Dayphase),
data = data,
na.action = na.fail,
family = Gamma(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
Now I want to plot the results of mod using plot(allEffects(mod)).
For plotting, I am backscaling my predictors in the allEffects-object by accessing
allEffects(mod)[["scaled_Minimal_Distance1"]][["x"]][["scaled_Minimal_Distance1"]] and doing as shown Here. I would also like to back-transform my response, to make the plot more understandable. Otherwise one would always have to keep in mind that 1 on the y-axis is actually 0, 2 is 1 etc. Can someone help me on how to do this, as I hit a roadblock and can't seem to figure it out myself.
Thank you very much in advance.
Related
How to run Latent Class Growth Modelling (LCGM) with a multinomial response variable in R (using the flexmix package)?
And how to stratify each class by a binary/categorical dependent variable?
The idea is to let gender shape the growth curve by cluster (cf. Mikolai and Lyons-Amos (2017, p. 194/3) where the stratification is done by education. They used Mplus)
I think I might have come close with the following syntax:
lcgm_formula <- as.formula(rel_stat~age + I(age^2) + gender + gender:age)
lcgm <- flexmix::stepFlexmix(.~ .| id,
data=d,
k=nr_of_classes, # would be 1:12 in real analysis
nrep=1, # would be 50 in real analysis to avoid local maxima
control = list(iter.max = 500, minprior = 0),
model = flexmix::FLXMRmultinom(lcgm_formula,varFix=T,fixed = ~0))
,which is close to what Wardenaar (2020,p. 10) suggests in his methodological paper for a continuous outcome:
stepFlexmix(.~ .|ID, k = 1:4,nrep = 50, model = FLXMRglmfix(y~ time, varFix=TRUE), data = mydata, control = list(iter.max = 500, minprior = 0))
The only difference is that the FLXMRmultinom probably does not support varFix and fixed parameters, altough adding them do produce different results. The binomial equivalent for FLXMRmultinom in flexmix might be FLXMRglm (with family="binomial") as opposed FLXMRglmfix so I suspect that the restrictions of the LCGM (eg. fixed slope & intercept per class) are not specified they way it should.
The results are otherwise sensible, but model fails to put men and women with similar trajectories in the same classes (below are the fitted probabilities for each relationship status in each class by gender):
We should have the following matches by cluster and gender...
1<->1
2<->2
3<->3
...but instead we have
1<->3
2<->1
3<->2
That is, if for example men in class one and women in class three would be forced in the same group, the created group would be more similar than the current first row of the plot grid.
Here is the full MVE to reproduce the code.
Got similar results with another dataset with diffent number of classes and up to 50 iterations/class. Have tried two alternative ways to predict the probabilities, with identical results. I conclude that the problem is most likely in the model specification (stepflexmix(...,model=FLXMRmultinom(...) or this is some sort of label switch issue.
If the model would be specified correctly and the issue is that similar trajectories for men/women end up in different classes, is there a way to fix that? By for example restricting the parameters?
Any assistance will be highly appreciated.
This seems to be a an identifiability issue apparently common in mixture modelling. In other words the labels are switched so that while there might not be a problem with the modelling as such, men and women end up in different groups and that will have to be dealt with one way or another
In the the new linked code, I have swapped the order manually and calculated the predictions with by hand.
Will be happy to hear, should someone has an alternative approach to deal with the label swithcing issue (like restricting parameters or switching labels algorithmically). Also curious if the model could/should be specified in some other way.
A few remarks:
I believe that this is indeed performing a LCGM as we do not specify random effects for the slopes or intercepts. Therefore I assume that intercepts and slopes are fixed within classes for both sexes. That would mean that the model performs LCGM as intended. By the same token, it seems that running GMM with random intercept, slope or both is not possible.
Since we are calculating the predictions by hand, we need to be able to separate parameters between the sexes. Therefore I also added an interaction term gender x age^2. The calculations seems to slow down somewhat, but the estimates are similar to the original. It also makes conceptually sense to include the interaction for age^2 if we have it for age already.
varFix=T,fixed = ~0 seem to be reduntant: specifying them do not change anything. The subsampling procedure (of my real data) was unaffected by the set.seed() command for some reason.
The new model specification becomes:
lcgm_formula <- as.formula(rel_stat~ age + I(age^2) +gender + age:gender + I(age^2):gender)
lcgm <- flexmix::flexmix(.~ .| id,
data=d,
k=nr_of_classes, # would be 1:12 in real analysis
#nrep=1, # would be 50 in real analysis to avoid local maxima (and we would use the stepFlexmix function instead)
control = list(iter.max = 500, minprior = 0),
model = flexmix::FLXMRmultinom(lcgm_formula))
And the plots:
I am using multivariate GAM models to learn more about fog trends in multiple regions. Fog is determined by visibility going below a certain threshold (< 400 meters). Our GAM model is used to determine the response of visibility to a range of meteorological variables.
However, my challenge right now is that I'd really like the y-axis to be the actual visibility observations rather than the centered smoothed. It is interesting to see how visibility is impacted by the covariates relative to the mean visibility in that location, but it's difficult to compare this for multiple locations where the mean visibility is different (and thus the 0 point in which visibility is enhanced or diminished has little comparable meaning).
In order to compare the results of multiple locations, I'm trying to make the y-axis actual visibility observations, and then I'll put a line at the visibility threshold we're interested in looking at (400 m)
to evaluate what the predictor variables values are like below that threshold (eg what temperatures are associated with visibility below 400 m).
I'm still a beginner when it comes to GAMs and R in general, but I've figured out a few helpful pieces so far.
Helpful things so far:
Attempt 1. how to extract gam fit for each variable in model
Extracting data used to make a smooth plot in mgcv
Attempt 2. how to use predict function to reconstruct a univariable model
http://zevross.com/blog/2014/09/15/recreate-the-gam-partial-regression-smooth-plots-from-r-package-mgcv-with-a-little-style/
Attempt 3. how to get some semblance of a y-axis that looks like visibility observations using "fitted" -- though I don't think this is
the correct approach since I'm not taking the intercept into account
http://gsp.humboldt.edu/OLM/R/05_03_GAM.html
simulated data
install.packages("mgcv") #for gam package
require(mgcv)
install.packages("pspline")
require(pspline)
#simulated GAM data for example
dataSet <- gamSim(eg=1,n=400,dist="normal",scale=2)
visibility <- dataSet[[1]]
temperature <- dataSet[[2]]
dewpoint <- dataSet[[3]]
windspeed <- dataSet[[4]]
#Univariable GAM model
gamobj <- gam(visibility ~ s(dewpoint))
plot(gamobj, scale=0, page=1, shade = TRUE, all.terms=TRUE, cex.axis=1.5, cex.lab=1.5, main="Univariable Model: Dew Point")
summary(gamobj)
AIC(gamobj)
abline(h=0)
Univariable Model of Dew Point
https://imgur.com/1uzP34F
ATTEMPT 2 -- predict function with univariable model, but didn't change y-axis
#dummy var that spans length of original covariate
maxDP <-max(dewpoint)
minDP <-min(dewpoint)
DPtrial.seq <-seq(minDP,maxDP,length=3071)
DPtrial.seq <-data.frame(dewpoint=DPtrial.seq)
#predict only the DP term
preds <- predict(gamobj, type="terms", newdata=DPtrial.seq, se.fit=TRUE)
#determine confidence intervals
DPplot <-DPtrial.seq$dewpoint
fit <-preds$fit
fit.up95 <-fit-1.96*preds$se.fit
fit.low95 <-fit+1.96*preds$se.fit
#plot
plot(DPplot, fit, lwd=3,
main="Reconstructed Dew Point Covariate Plot")
#plot confident intervals
polygon(c(DPplot, rev(DPplot)),
c(fit.low95,rev(fit.up95)), col="grey",
border=NA)
lines(DPplot, fit, lwd=2)
rug(dewpoint)
Reconstructed Dew Point Covariate Plot
https://imgur.com/VS8QEcp
ATTEMPT 3 -- changed y-axis using "fitted" but without taking intercept into account
plot(dewpoint,fitted(gamobj), main="Fitted Response of Y (Visibility) Plotted Against Dew Point")
abline(h=mean(visibility))
rug(dewpoint)
Fitted Response of Y Plotted Against Dew Point https://imgur.com/RO0q6Vw
Ultimately, I want a horizontal line where I can investigate the predictor variable relative to 400 meters, rather than just the mean of the response variable. This way, it will be comparable across multiple sites where the mean visibility is different. Most importantly, it needs to be for multiple covariates!
Gavin Simpson has explained the method in a couple of posts but unfortunately, I really don't understand how I would hold the mean of the other covariates constant as I use the predict function:
Changing the Y axis of default plot.gam graphs
Any deeper explanation into the method for doing this would be super helpful!!!
I'm not sure how helpful this will be as your Q is a little more open ended than we'd typically like on SO, but, here goes.
Firstly, I think it would help to think about modelling the response variable, which I assume is currently visibility. This is going to be a continuous variable, bounded at 0 (perhaps the data never reach zero?) which suggests modelling the data as conditionally distributed either
gamma (family = Gamma(link = 'log')) for visibility that never takes a value of zero.
Tweedie (family = tw()) for data that do have zeroes.
An alternative approach would be to model the occurrence of fog; if this is defined as an event <400m visibility then you could turn all your observations into 0/1 values for being a fog event or otherwise. Then you'd model the data as conditionally distributed Bernoulli, using family = binomial().
Having decided on a modelling approach, we need to model the response. This should be done using a multiple regression type of approach, with a GAM including multiple predictors. This way you get to estimate the effect of each potential predictor variable on the response while controlling for the effects of the other predictors. If you just do this using a single predictor at a time, say dewpoint, that variable could well "explain" variation in the data that might be due to another predictor, windspeed say, and you wouldn't know it.
Furthermore, there may well be interactions between predictors that you'll want to control for if they exist, which can only be done in
Then, to finally get to the crux of your problem, having fitted the multi-predictor model to "explain" visibility, you will need to predict from the model for sets of likely conditions. To look at how the visibility varies with dewpoint in a model where other predictor variables have effects, you need to fix the other variables at some reasonable values; one option is to set them to their mean (or modal value in the case of any factor predictor variables), or some other value indicative of typically values for that variable. You'll have to use your domain knowledge for this.
If you have interactions in the model, then you'll need to vary the two variables in the interaction, whilst holding all other variable fixed at some values.
Let's assume you don't have interactions and are interested in dewpoint but the model also includes windspeed. The mean windspeed for the values used to fit the model can be found from the cmX component of the fitted model. Of you could just calculate this from the observed windpseed values or set it to some known number you want to use. Denote the fitted by m, and the data frame with your data in it by df, then we can create new data to predict at over the range of dewpoint, whilst holding windspeed fixed.
mn.windspd <- m$cmX['windspeed']
## or
mn.windspd <- with(df, mean(windspeed))
## or set it some some value
mn.windspd <- 10 # say
Then you can do
preddata <- with(df,
expand.grid(dewpoint = seq(min(dewpoint),
max(dewpoint),
length = 300),
windspeed = mn.windspd))
Then you use this to predict from the fitted model:
pred <- predict(m, newdata = preddata, type = "link", se.fit = TRUE)
pred <- as.data.frame(pred)
Now we want to put these predictions back on to the response scale, and we want a confidence interval so we have to create that first before back transforming:
ilink <- family(m)$linkinv
pred <- transform(pred,
Fitted = ilink(fit),
Upper = ilink(fit + (2 * se.fit)),
Lower = ilink(fit - (2 * se.fit)),
dewpoint = preddata = dewpoint)
Now you can visualised the effect of dewpoint on the response whilst keeping windspeed fixed.
In your case, you will have to extend this to keeping temperature constant also, but that is done in the same way
mn.windspd <- m$cmX['windspeed']
mn.temp <- m$cmX['temperature']
preddata <- with(df,
expand.grid(dewpoint = seq(min(dewpoint),
max(dewpoint),
length = 300),
windspeed = mn.windspd,
temperature = mn.temp))
and then follow the steps above to do the prediction.
For one or two variables varying I have a function data_slice() in my gratia package which will do the above expand.grid() stuff for you so you don't have to specify the mean values of the other covariates:
preddata <- data_slice(m, 'dewpoint', n = 300)
technically this finds the value in the data closest to the median value (for the covariates not varying). If you want means, then do
fixdf <- data.frame(windspeed = mn.windspd, temperature = mn.temp)
preddata <- data_slice(m, 'dewpoint', data = fixdf, n = 300)
If you have an interaction, say between dewpoint and windspeed then you need to vary two variables. This is pretty easy again with expand.grid():
mn.temp <- m$cmX['temperature']
preddata <- with(df,
expand.grid(dewpoint = seq(min(dewpoint),
max(dewpoint),
length = 100),
windspeed = seq(min(windspeed),
max(windspeed),
length = 300),
temperature = mn.temp))
This will create a 100 x 100 grid of values of the covariates to predict at, whilst holding temperature constant.
For data_slice() you'd need to do:
fixdf <- data.frame(temperature = mn.temp)
preddata <- data_slice(m, 'dewpoint', 'windpseed',
data = fixdf, n = 300)
And extending this on to more covariates you want to vary, is also easy following this pattern with expand.grid(); I have yet to implement more than 2 variables varying in data_slice.
Here is the plot of the initial data (after performing a log transformation).
It is evident there is both a linear trend as well as a seasonal trend. I can address both of these by taking the first and twelfth (seasonal) difference: diff(diff(data), 12). After doing so, here is the plot of the resulting data
.
This data does not look great. While the mean in constant, we see a funneling effect as time progresses. Here are the ACF/PACF:.
Any suggestions for possible fits to try. I used the auto.arima() function which suggested an ARIMA(2,0,2)xARIMA(1,0,2)(12) model. However, once I took the residuals from the fit, it was clear there was still some sort of structure in them. Here is the plot of the residuals from the fit as well as the ACF/PACF of the residuals.
There does not appear to be a seasonal pattern regarding which lags have spikes in the ACF/PACF of residuals. However, this is still something not captured by the previous steps. What do you suggest I do? How could I go about building a better model that has better model diagnostics (which at this point is just a better looking ACF and PACF)?
Here is my simplified code thus far:
library(TSA)
library(forecast)
beer <- read.csv('beer.csv', header = TRUE)
beer <- ts(beer$Production, start = c(1956, 1), frequency = 12)
# transform data
boxcox <- BoxCox.ar(beer) # 0 in confidence interval
beer.log <- log(beer)
firstDifference <- diff(diff(beer.log), 12) # get rid of linear and
# seasonal trend
acf(firstDifference)
pacf(firstDifference)
eacf(firstDifference)
plot(armasubsets(firstDifference, nar=12, nma=12))
# fitting the model
auto.arima(firstDifference, ic = 'bic') # from forecasting package
modelFit <- arima(firstDifference, order=c(1,0,0),seasonal
=list(order=c(2, 0, 0), period = 12))
# assessing model
resid <- modelFit$residuals
acf(resid, lag.max = 15)
pacf(resid, lag.max = 15)
Here is the data, if interested (I think you can use an html to csv converter if you would like): https://docs.google.com/spreadsheets/d/1S8BbNBdQFpQAiCA4J18bf7PITb8kfThorMENW-FRvW4/pubhtml
Jane,
There are a few things going on here.
Instead of logs, we used the tsay variance test which shows that the variance increased after period 118. Weighted least squares deals with it.
March becomes higher beginning at period 111. An alternative to an ar12 or seasonal differencing is to identify seasonal dummies. We found that 7 of the 12 months were unusual with a couple level shifts, an AR2 with 2 outliers.
Here is the fit and forecasts.
Here are the residuals.
ACF of residuals
Note: I am a developer of the software Autobox. All models are wrong. Some are useful.
Here is Tsay's paper
http://onlinelibrary.wiley.com/doi/10.1002/for.3980070102/abstract
I have an issue with Random Forest with the Importance / varImPlot function, I hope someone could help me with?
I tried to code versions but I am confused about the (different) results:
1.)
rffit = randomForest(price~.,data=train,mtry=x,ntree=500)
rfvalpred = predict(rffit,newdata=test)
varImpPlot(rffit)
importance(rffit)
Shows the plot and the data of “importance”, however only “IncNodePurity”. And the data is different the plot and the data, I tried with "Scale" but did not work.
2.)
rf.analyzed_data = randomForest(price~.,data=train,mtry=x,ntree=500,importance=TRUE)
yhat.rf = predict(rf.analyzed_data,newdata=test)
varImpPlot(rf.analyzed_data)
importance(rf.analyzed_data)
In that case it does not produce any plot anymore and the importance data is showing “%IncMSE” and “IncNodePurity” data but the “IncNodePurity” data is different to first code?
Questions:
1.) Any idea why data is different for “IncNodePurity”?
2.) Any idea why no “%IncMSE” is shown in the first version?
3.) Why no plot is shown in the second version?
Many thanks!!
Ed
1) IncNodePurity is derived from the loss function, and you get that measure for free just by training the model. On the downside it is a more unstable estimate as results may vary from each model run. It is also more biased as it favors variables with many levels. I guess your found the differences are due to randomness.
2) VI, %IncMSE takes a little extra time to compute and is therefore optional. Roughly all values in data set needs to be shuffled and every OOB sample needs to be predicted once for every tree times for every variable. As the package randomForest is designed, you have to compute VI during training. importance must be set to TRUE. varImpPlot cannot plot it as it has not been computed.
3) Not sure. In this code example I see both plots at least.
library(randomForest)
#data
X = data.frame(replicate(6,rnorm(1000)))
y = with(X, X1^2 + sin(X2*pi) + X3*X4)
train = data.frame(y=y,X=X)
#training
rf1=randomForest(y~.,data=train,importance=F)
rf2=randomForest(y~.,data=train, importance=T)
#plotting importnace
varImpPlot(rf1) #plot only with IncNodePurity
varImpPlot(rf2) #bi-plot also with %IncMSE
So I am currently trying to draw the confidence interval for a linear model. I found out I should use predict.lm() for this, but I have a few problems really understanding the function and I do not like using functions without knowing what's happening. I found several how-to's on this subject, but only with the corresponding R-code, no real explanation.
This is the function itself:
## S3 method for class 'lm'
predict(object, newdata, se.fit = FALSE, scale = NULL, df = Inf,
interval = c("none", "confidence", "prediction"),
level = 0.95, type = c("response", "terms"),
terms = NULL, na.action = na.pass,
pred.var = res.var/weights, weights = 1, ...)
Now, what I've trouble understanding:
1) newdata
An optional data frame in which to look for variables
with which to predict. If omitted, the fitted values are used.
Everyone seems to use newdata for this, but I cannot quite understand why. For calculating the confidence interval I obviously need the data which this interval is for (like the # of observations, mean of x etc), so cannot be what is meant by it. But then: What is does it mean?
2) interval
Type of interval calculation.
okay.. but what is "none" for?
3a) type
Type of prediction (response or model term).
3b) terms
If type="terms", which terms (default is all terms)
3a: Can I by that get the confidence interval for one specific variable in my model? And if so, what is 3b for then? If I can specify the term in 3a, it wouldn't make sense to do it in 3b again.. so I guess I'm wrong again, but I cannot figure out why.
I guess some of you might think: Why don't just try this out? And I would (even if it would maybe not solve everything here), but I right now don't know how to. As I do not now what the newdata is for, I don't know how to use it and if I try, I do not get the right confidence interval. Somehow it is very important how you choose that data, but I just don't understand!
EDIT: I want to add that my intention is to understand how predict.lm works. By that I mean I don't understand if it works the way I think it does. That is it calculates y-hat (predicted values) and than uses adds/subtracts for each the upr/lwr-bounds of the interval to calculate several datapoints(looking like a confidence-line then) ?? Then I would undestand why it is necessary to have the same lenght in the newdata as in the linear model.
Make up some data:
d <- data.frame(x=c(1,4,5,7),
y=c(0.8,4.2,4.7,8))
Fit the model:
lm1 <- lm(y~x,data=d)
Confidence and prediction intervals with the original x values:
p_conf1 <- predict(lm1,interval="confidence")
p_pred1 <- predict(lm1,interval="prediction")
Conf. and pred. intervals with new x values (extrapolation and more finely/evenly spaced than original data):
nd <- data.frame(x=seq(0,8,length=51))
p_conf2 <- predict(lm1,interval="confidence",newdata=nd)
p_pred2 <- predict(lm1,interval="prediction",newdata=nd)
Plotting everything together:
par(las=1,bty="l") ## cosmetics
plot(y~x,data=d,ylim=c(-5,12),xlim=c(0,8)) ## data
abline(lm1) ## fit
matlines(d$x,p_conf1[,c("lwr","upr")],col=2,lty=1,type="b",pch="+")
matlines(d$x,p_pred1[,c("lwr","upr")],col=2,lty=2,type="b",pch=1)
matlines(nd$x,p_conf2[,c("lwr","upr")],col=4,lty=1,type="b",pch="+")
matlines(nd$x,p_pred2[,c("lwr","upr")],col=4,lty=2,type="b",pch=1)
Using new data allows for extrapolation beyond the original data; also, if the original data are sparsely or unevenly spaced, the prediction intervals (which are not straight lines) may not be well approximated by linear interpolation between the original x values ...
I'm not quite sure what you mean by the "confidence interval for one specific variable in my model"; if you want confidence intervals on a parameter, then you should use confint. If you want predictions for the changes based only on some of the parameters changing (ignoring the uncertainty due to the other parameters), then you do indeed want to use type="terms".
interval="none" (the default) just tells R not to bother computing any confidence or prediction intervals, and to return just the predicted values.