I am interested in using the new bvar package in R to predict a set of endogenous time series. However, because of the COVID pandemic, my time series have been through a structural break. What is the best way to account for this in the model? Some hypotheses:
Add exogenous dummy variable (it seems the package doesn't have this feature)
Add endogenous dummy variable with strong priors that zero the coefficients of impact from other variables over it (i.e. an "artificial" exogenous variable)
Create two separate models (before vs after structural break)
I have tried a mix of 2+3. I tested a (i) model with only recent data (after structural break) and no dummies vs (ii) another with the full history with an additional endogenous (dummy) variable, but without the strong dummy prior (I couldn't understand how to configure it properly). The model (ii) has performed way better in the test set.
I wrote an e-mail to the owner of the package, Nikolas Kuschnig (couldn't find his user in SO), to which he replied:
Structural breaks are always a pain to model. In general it's probably
preferable to estimate two separate models, but given the short timespan and you
getting usable results your idea with adding a dummy variable should also work.
You can adjust priors from other variables by manually setting psi in
bv_mn() (see the docs and the vignette for an explanation).
Depending on the variables you might also be fine not doing any of that, since
COVID could just be seen as another shock (which is almost always quite the
stretch, given the extent of it).
Note that if there is an actual structural break, the dummies won't suffice,
since the coefficients would change (hence my preference for your option 3). To
an extent you could model this with a Markov-switching VAR, but unfortunately I
don't know of an accessible implementation for R.
Thank you, Nikolas
Related
I have a dataset in which individuals, each belonging to a particular group, repeatedly chose between multiple discrete outcomes.
subID group choice
1 Big A
1 Big B
2 Small B
2 Small B
2 Small C
3 Big A
3 Big B
. . .
. . .
I want to test how group membership influences choice, and want to account for non-independence of observations due to repeated choices being made by the same individuals. In turn, I planned to implement a mixed multinomial regression treating group as a fixed effect and subID as a random effect. It seems that there are a few options for multinomial logits in R, and I'm hoping for some guidance on which may be most easily implemented for this mixed model:
1) multinom - GLM, via nnet, allows the usage of the multinom function. This appears to be a nice, clear, straightforward option... for fixed effect models. However is there a manner to implement random effects with multinom? A previous CV post suggests that multinom is able to handle mixed-effects GLM with poisson distribution and a log link. However, I don't understand (a) why this is the case or (b) the required syntax. Can anyone clarify?
2) mlogit - A fantastic package, with incredibly helpful vignettes. However, the "mixed logit" documentation refers to models that have random effects related to alternative specific covariates (implemented via the rpar argument). My model has no alternative specific variables; I simply want to account for the random intercepts of the participants. Is this possible with mlogit? Is that variance automatically accounted for by setting subID as the id.var when shaping the data to long form with mlogit.data? EDIT: I just found an example of "tricking" mlogit to provide random coefficients for variables that vary across individuals (very bottom here), but I don't quite understand the syntax involved.
3) MCMCglmm is evidently another option. However, as a relative novice with R and someone completely unfamiliar with Bayesian stats, I'm not personally comfortable parsing example syntax of mixed logits with this package, or, even following the syntax, making guesses at priors or other needed arguments.
Any guidance toward the most straightforward approach and its syntax implementation would be thoroughly appreciated. I'm also wondering if the random effect of subID needs to be nested within group (as individuals are members of groups), but that may be a question for CV instead. In any case, many thanks for any insights.
I would recommend the Apollo package by Hess & Palma. It comes with a great documentation and a quite helpful user group.
I'm working with a large longitudinal dataset of firm-year observations. For some time now I have been using lme4to implement crossed (non-nested) effects for year and firm-ID groups.
My goal is now to correct for the serial correlation in the firm-group dimension. Based on chl's and fabians' answers to this question (as well as Ben Bolker's comment on the latter), I've assumed this is impossible with lmer(), but is feasible with nlme::lme().
I have been able to implement crossed effects in nlme based on the discussion in Pinheiro & Bates (2000, sec. 4.2.2, pp. 163-6). In principle then, I believe I can use the correlation = AR1() speficiation in lme() to control for autocorrelation.
My strong preference, however, would be to implement such a correlation specification in lmer() because:
lme4 is much, much (much) faster
nlme requires crossed effects to be nested in some higher group -- without such a higher level grouping I'm forced to create an arbitrary dummy for groupedData to which all observations belong (e.g., here). This creates issues interpreting the relative levels of variation between the two crossed groups and the residual variance because some of the variation appears to be captured by the higher-level dummy group.
I got excited when I found the feature request #224 on GitHub, but alas it doesn't seem like there's much movement on the flexLambda front (please let me know if I'm wrong!).
lme4 v1.1-10
I've just noticed that the latest (Oct. 2015) version of lme4 contains a vcconv command that can
Convert between representation of (co-)variance structures (EXPERIMENTAL.)
Based on the source code, it seems that maybe the sdcor2cov option could allow one to specify a correlation structure such as AR(1).
So my questions are:
Is this interpretation of the vcconv function correct?
If so, does the user supply the correlation (e.g., AR(1)) parameters or are they determined internally in lmer()?
How does one implement this function properly?
In the last few months I've worked on a number of projects where I've used the glmnet package to fit elastic net models. It's great, but the interface is rather bare-bones compared to most R modelling functions. In particular, rather than specifying a formula and data frame, you have to give a response vector and predictor matrix. You also lose out on many quality-of-life things that the regular interface provides, eg sensible (?) treatment of factors, missing values, putting variables into the correct order, etc.
So I've generally ended up writing my own code to recreate the formula/data frame interface. Due to client confidentiality issues, I've also ended up leaving this code behind and having to write it again for the next project. I figured I might as well bite the bullet and create an actual package to do this. However, a couple of questions before I do so:
Are there any issues that complicate using the formula/data frame interface with elastic net models? (I'm aware of standardisation and dummy variables, and wide datasets maybe requiring sparse model matrices.)
Is there any existing package that does this?
Well, it looks like there's no pre-built formula interface, so I went ahead and made my own. You can download it from Github: https://github.com/Hong-Revo/glmnetUtils
Or in R, using devtools::install_github:
install.packages("devtools")
library(devtools)
install_github("hong-revo/glmnetUtils")
library(glmnetUtils)
From the readme:
Some quality-of-life functions to streamline the process of fitting
elastic net models with glmnet, specifically:
glmnet.formula provides a formula/data frame interface to glmnet.
cv.glmnet.formula does a similar thing for cv.glmnet.
Methods for predict and coef for both the above.
A function cvAlpha.glmnet to choose both the alpha and lambda parameters via cross-validation, following the approach described in
the help page for cv.glmnet. Optionally does the cross-validation in
parallel.
Methods for plot, predict and coef for the above.
Incidentally, while writing the above, I think I realised why nobody has done this before. Central to R's handling of model frames and model matrices is a terms object, which includes a matrix with one row per variable and one column per main effect and interaction. In effect, that's (at minimum) roughly a p x p matrix, where p is the number of variables in the model. When p is 16000, which is common these days with wide data, the resulting matrix is about a gigabyte in size.
Still, I haven't had any problems (yet) working with these objects. If it becomes a major issue, I'll see if I can find a workaround.
Update Oct-2016
I've pushed an update to the repo, to address the above issue as well as one related to factors. From the documentation:
There are two ways in which glmnetUtils can generate a model matrix out of a formula and data frame. The first is to use the standard R machinery comprising model.frame and model.matrix; and the second is to build the matrix one variable at a time. These options are discussed and contrasted below.
Using model.frame
This is the simpler option, and the one that is most compatible with other R modelling functions. The model.frame function takes a formula and data frame and returns a model frame: a data frame with special information attached that lets R make sense of the terms in the formula. For example, if a formula includes an interaction term, the model frame will specify which columns in the data relate to the interaction, and how they should be treated. Similarly, if the formula includes expressions like exp(x) or I(x^2) on the RHS, model.frame will evaluate these expressions and include them in the output.
The major disadvantage of using model.frame is that it generates a terms object, which encodes how variables and interactions are organised. One of the attributes of this object is a matrix with one row per variable, and one column per main effect and interaction. At minimum, this is (approximately) a p x p square matrix where p is the number of main effects in the model. For wide datasets with p > 10000, this matrix can approach or exceed a gigabyte in size. Even if there is enough memory to store such an object, generating the model matrix can take a significant amount of time.
Another issue with the standard R approach is the treatment of factors. Normally, model.matrix will turn an N-level factor into an indicator matrix with N-1 columns, with one column being dropped. This is necessary for unregularised models as fit with lm and glm, since the full set of N columns is linearly dependent. With the usual treatment contrasts, the interpretation is that the dropped column represents a baseline level, while the coefficients for the other columns represent the difference in the response relative to the baseline.
This may not be appropriate for a regularised model as fit with glmnet. The regularisation procedure shrinks the coefficients towards zero, which forces the estimated differences from the baseline to be smaller. But this only makes sense if the baseline level was chosen beforehand, or is otherwise meaningful as a default; otherwise it is effectively making the levels more similar to an arbitrarily chosen level.
Manually building the model matrix
To deal with the problems above, glmnetUtils by default will avoid using model.frame, instead building up the model matrix term-by-term. This avoids the memory cost of creating a terms object, and can be noticeably faster than the standard approach. It will also include one column in the model matrix for all levels in a factor; that is, no baseline level is assumed. In this situation, the coefficients represent differences from the overall mean response, and shrinking them to zero is meaningful (usually).
The main downside of not using model.frame is that the formula can only be relatively simple. At the moment, only straightforward formulas like y ~ x1 + x2 + ... + x_p are handled by the code, where the x's are columns already present in the data. Interaction terms and computed expressions are not supported. Where possible, you should compute such expressions beforehand.
Update Apr-2017
After a few hiccups, this is finally on CRAN.
I am trying to analyze a panel data which includes observations for each US state collected across 45 years.
I have two predictor variables that vary across time (A,B) and one that does not vary (C). I am especially interested in knowing the effect of C on the dependent variable Y, while controlling for A and B, and for the differences across states and time.
This is the model that I have, using plm package in R.
random <- plm(Y~log1p(A)+B+C, index=c("state","year"),model="random",data=data)
My reasoning is that with a time invariant variable I should be using random rather than fixed effect model.
My question is: Is my model and thinking correct?
Thank you for your help in advance.
You base your answer about the decision between fixed and random effect soley on computational grounds. Please see the specific assumptions associated with the different models. The Hausman test is often used to discriminate between the fixed and the random effects model, but should not be taken as the definite answer (any good textbook will have further details).
Also pooled OLS could yield a good model, if it applies. Computationally, pooled OLS will also give you estimates for time-invariant variables.
I want to do a structural equation model for my analysis.
All three concepts are formative, which means these measurement variables construct the latent structure. Not reflective.
And also I want to control for demographic variables.
The analysis will use R and I learnt Lavaan in statistics class, just curious whether anyone can give more information on what I want to do.
Thanks ahead.
in order to used formative constructs you need to use partial least square SEM (PLS-SEM) and not covariance based SEM (Cov-SEM).
the underlying assumption of the two technique differs, as PLS assumes that because the constructs are formative there is no error in measurement while CoV-SEM, has the defaults assumption of reflexive measurement and thus takes into account the error terms while analyzing the model
Lavaan package is a COV-SEM one, you can try plspm for using formative items
here there is a guide on how to use the plspm pakage:
http://gastonsanchez.com/PLS_Path_Modeling_with_R.pdf