I have a dataset with data left censored and I wanted to apply a multilevel mixed-effects tobit regression, but I only find information about how to do it in Stata. Is it possible to do it in R?
I found the packages 'VGAM' and 'CensREG', but I don't get how to add fixed and random effects.
Also my data is log-normal distributed, is there a way to add this to the model?
Thanks!
According to Section 3.5 of a vignette, the censReg package can handle a mixed model if the data are prepared properly via the plm package.
This Cross Validated page shows an example.
I don't have experience with this; it might only work with formal panel data rather than more general random-effects structures.
If your data are truly log-normal, you could take logs first and set the lower censoring limit on the log scale. Note that an apparent log-normal distribution of outcomes might just represent a corresponding distribution of predictor values with an underlying normal error distribution around the predictions. Don't jump blindly into a log-normal assumption.
We are due to collect some survey data that has a range 0-15 score, potentially skewed, and has a multilevel structure (repeated measures and clustering). I'm anticipating that fitting a linear mixed model in R lmer will be problematic given the outcome distribution.
I am considering whether some sort of right-censored generalized linear mixed model (Poisson) may be a solution but I'm struggling to find something to fit this model.
I think the closest that I can find is the VGAM::vglm with family = cens.poisson but, as far as I can tell, it cannot include multilevel structure?
Does anyone know any R functions that would permit this model? If so, is there an equivalent power calc function or would this be written as a simulation?
I am trying to investigate the relationship between some Google Trends Data and Stock Prices.
I performed the augmented ADF Test and KPSS test to make sure that both time series are integrated of the same order (I(1)).
However, after I took the first differences, the ACF plot was completely insigificant (except for 1 of course), which told me that the differenced series are behaving like white noise.
Nevertheless I tried to estimate a VAR model which you can see attached.
As you can see, only one constant is significant. I have already read that because Stocks.ts.l1 is not significant in the equation for GoogleTrends and GoogleTrends.ts.l1 is not significant in the equation for Stocks, there is no dynamic between the two time series and both can also be models independently from each other with a AR(p) model.
I checked the residuals of the model. They fulfill the assumptions (normally distributed residuals are not totally given but ok, there is homoscedasticity, its stable and there is no autocorrelation).
But what does it mean if no coefficient is significant as in the case of the Stocks.ts equation? Is the model just inappropriate to fit the data, because the data doesn't follow an AR process. Or is the model just so bad, that a constant would describe the data better than the model? Or a combination of the previous questions? Any suggestions how I could proceed my analysis?
Thanks in advance
I'm new to time series and used the monthly ozone concentration data from Rob Hyndman's website to do some forecasting.
After doing a log transformation and differencing by lags 1 and 12 to get rid of the trend and seasonality respectively, I plotted the ACF and PACF shown [in this image][2]. Am I on the right track and how would I interpret this as a SARIMA?
There seems to be a pattern every 11 lags in the PACF plot, which makes me think I should do more differencing (at 11 lags), but doing so gives me a worse plot.
I'd really appreciate any of your help!
EDIT:
I got rid of the differencing at lag 1 and just used lag 12 instead, and this is what I got for the ACF and PACF.
From there, I deduced that: SARIMA(1,0,1)x(1,1,1) (AIC: 520.098)
or SARIMA(1,0,1)x(2,1,1) (AIC: 521.250)
would be a good fit, but auto.arima gave me (3,1,1)x(2,0,0) (AIC: 560.7) normally and (1,1,1)x(2,0,0) (AIC: 558.09) without stepwise and approximation.
I am confused on which model to use, but based on the lowest AIC, SAR(1,0,1)x(1,1,1) would be the best? Also, the thing that concerns me is that none of the models pass the Ljung-Box test. Is there any way I can fix this?
It is quite difficult to manually select a model order that will perform well at forecasting a dataset. This is why Rob has built the 'auto.arima' function in his R forecast package, to figure out the model that may perform best based on certain metrics.
When you see a pacf plot with significantly negative lags that usually means you have over differenced your data. Try removing the 1st order difference and keeping the 12 order difference. Then carry on making your best guess.
I'd recommend trying his auto.arima function and passing it a time series object with frequency = 12. He has a good writeup of seasonal arima models here:
https://www.otexts.org/fpp/8/9
If you would like more insight into manually selecting a SARIMA model order, this is a good read:
https://onlinecourses.science.psu.edu/stat510/node/67
In response to your Edit:
I think it would be beneficial to this post if you clarify your objective. Which of the following are you trying to achieve?
Find a model where residuals satisfy Ljung Box Test
Produce the most accurate out of sample forecast
Manually select lag orders such that ACF and PACF plots show no significant lags remaining.
In my opinion, #2 is the most sought after objective so I'll assume that is your goal. From my experience, #3 produces poor results out of sample. In regards to #1, I am usually not concerned about correlations remaining in the residuals. We know we do not have the true model for this time-series, so I do not feel there's any reason to expect an approximate model that performs well out of sample to not have left something behind in the residuals that is more complex perhaps, or nonlinear etc.
To provide you another SARIMA result, I ran this data through some code I've developed and found the following equation produced the minimal error on a cross-validation period.
Final model is:
SARIMA [0,1,1] [1,1,1]12 with a constant using the log normal of the time-series.
The errors in the cross validation period are:
MAPE = 16%
MAE = 0.46
RSQR = 74%
Here is the Partial Autocorrelation plot of the residuals for your information.
This is roughly similar in methodology to selecting an equation based on AICc to my understanding, but is ultimately a different approach. Regardless, if your objective is out of sample accuracy, I'd recommend evaluating equations in terms of their out of sample accuracy versus in-sample fit, tests, or plots.
I have a data structure with binary 0-1 variable (click & Purchase; click & not-purchase) against a vector of the attributes. I used logistic regression to get the probabilities of the purchase. How can I use Random Forest to get the same probabilities? Is it by using Random Forest regression? or is it Random Forest classification with type='prob' in R which gives the probability of categorical variable?
It won't give you the same result since the structure of the two method are different. Logistic regression is given by a definitive linear specification, where RF is a collective vote from multiple independent/random trees. If specification and input feature are properly tuned for both, they can produce comparable results. Here is the major difference between the two:
RF will give more robust fit against noise, outliers, overfitting or multicollinearity etc which are common pitfalls in regression type of solution. Basically if you don't know or don't want to know much about whats going in with the input data, RF is a good start.
logistic regression will be good if you know expertly about the data and how to properly specify the equation. Or somehow want to engineer how the fit/prediction works. The explicit form of GLM specification will allow you to do that.