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.
Related
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 have a collection of documents, that might have latent topics associated with them. It is likely that each document might relate to one or more topics. I have a master file of all possible "topics"/categories and descriptions to these topics. I am seeking to create a model that predicts the topics for each document.
I could potentially use Supervised text classification using RTextTools, but that would only help me categorize documents to belong to one category or another. I am seeking to find a solution that would not only help me determine the topic proportions to the document, but also give the term-topic/category distributions.
sLDA seems like a good fit, but it seems to only predict continuous variable outcomes instead of categorical.
LDA is more of a classification method, predicting classes. other methods can be multinational logistic regression. LDA could be harder to train compared to Multinational, given a possible little improved fit it can provide.
update: LDA is a classification method where unlike logistic regression that you directly predict Pr(Y = k|X = x) using the logit link, LDA uses the Bayes theorem for prediction. It is normally a more popular compared to logistic regression (and its extension for multi-class prediction, namely multinational logistic regression) for multi-class problems.
LDA assumes that the observations are drawn from a Gaussian distribution with a common covariance matrix in each class, and so can provide some improvements over logistic regression when this assumption approximately holds. in contrast,it is suggested that logistic regression can outperform LDA if these Gaussian assumptions are not hold. To sum up, While both are appropriate for the development of linear classification models, linear discriminant analysis makes more assumptions about the underlying data as opposed to logistic regression, which makes logistic regression a more flexible and robust method when these assumptions are not hold. So what I meant was, it is important to understand your data well, and see which might fit your data better. There are good sources on read you can read and comparison of classification methods:
http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Seventh%20Printing.pdf
I suggest Introduction to statistical learning, on classification chapter. Hope this helps
I want to compare the curve fits of three models by r-squared values. I ran models using the nls and drc packages. It appears, though, that neither of those packages calculate r-squared values; they give "residual std error" and "residual sum of squares" though.
Can these two be used to compare model fits?
This is really a statistics question, rather than a coding question: consider posting on stats.stackexchange.com; you're likely to get a better answer.
RSQ is not really meaningful for non-linear regression. This is why summary.nls(...) does not provide it. See this post for an explanation.
There is a common, and understandable, tendency to hope for a single statistic that allows one to assess which of a set of models better fits a dataset. Unfortunately, it doesn't work that way. Here are some things to consider.
Generally, the best model is the one that has a mechanistic underpinning. Do your models reflect some physical process, or are you just trying a bunch of mathematical equations and hoping for the best? The former approach almost always leads to better models.
You should consider how the models will be used. Will you be interpolating (e.g. estimating y|x within the range of your dataset), or will you be extrapolating (estimating y|x outside the range of your data)? Some models yield a fit that provides relatively accurate estimates slightly outside the dataset range, and others completely fall apart.
Sometimes the appropriate modeling technique is suggested by the type of data you have. For example, if you have data that counts something, then y is likely to be poisson distributed and a generalized linear model (glm) in the poisson family is indicated. If your data is binary (e.g. only two possible outcomes, success or failure), then a binomial glm is indicated (so-called logistic regression).
The key underlying assumption of least squares techniques is that the error in y is normally distributed with mean 0 and constant variance. We can test this after doing the fit by looking at a plot of standardized residuals vs. y, and by looking at a Normal Q-Q plot of the residuals. If the residuals plot shows scatter increasing or decreasing with y then the model in not a good one. If the Normal Q-Q plot is not close to a straight line, then the residuals are not normally distributed and probably a different model is indicated.
Sometimes certain data points have high leverage with a given model, meaning that the fit is unduly influenced by those points. If this is a problem you will see it in a leverage plot. This indicates a weak model.
For a given model, it may be the case that not all of the parameters are significantly different from 0 (e.g., p-value of the coefficient > 0.05). If this is the case, you need to explore the model without those parameters. With nls, this often implies a completely different model.
Assuming that your model passes the tests above, it is reasonable to look at the F-statistic for the fit. This is essentially the ratio of SSR/SSE corrected for the dof in the regression (R) and the residuals (E). A model with more parameters will generally have smaller residual SS, but that does not make it a better model. The F-statistic accounts for this in that models with more parameters will have larger regression dof and smaller residual dof, making the F-statistic smaller.
Finally, having considered the items above, you can consider the residual standard error. Generally, all other things being equal, smaller residual standard error is better. Trouble is, all other things are never equal. This is why I would recommend looking at RSE last.
What functions do you use in R to fit a curve to your data and test how well that curve fits? What results are considered good?
Just the first part of that question can fill entire books. Just some quick choices:
lm() for standard linear models
glm() for generalised linear models (eg for logistic regression)
rlm() from package MASS for robust linear models
lmrob() from package robustbase for robust linear models
loess() for non-linear / non-parametric models
Then there are domain-specific models as e.g. time series, micro-econometrics, mixed-effects and much more. Several of the Task Views as e.g. Econometrics discuss this in more detail. As for goodness of fit, that is also something one can spend easily an entire book discussing.
The workhorses of canonical curve fitting in R are lm(), glm() and nls(). To me, goodness-of-fit is a subproblem in the larger problem of model selection. Infact, using goodness-of-fit incorrectly (e.g., via stepwise regression) can give rise to seriously misspecified model (see Harrell's book on "Regression Modeling Strategies"). Rather than discussing the issue from scratch, I recommend Harrell's book for lm and glm. Venables and Ripley's bible is terse, but still worth a reading. "Extending the Linear Model with R" by Faraway is comprehensive and readable. nls is not covered in these sources, but "Nonlinear Regression with R" by Ritz & Streibig fills the gap and is very hands-on.
The nls() function (http://sekhon.berkeley.edu/stats/html/nls.html) is pretty standard for nonlinear least-squares curve fitting. Chi squared (the sum of the squared residuals) is the metric that is optimized in that case, but it is not normalized so you can't readily use it to determine how good the fit is. The main thing you should ensure is that your residuals are normally distributed. Unfortunately I'm not sure of an automated way to do that.
The Quick R site has a reasonable good summary of basic functions used for fitting models and testing the fits, along with sample R code:
http://www.statmethods.net/stats/regression.html
The main thing you should ensure is
that your residuals are normally
distributed. Unfortunately I'm not
sure of an automated way to do that.
qqnorm() could probably be modified to find the correlation between the sample quantiles and the theoretical quantiles. Essentially, this would just be a numerical interpretation of the normal quantile plot. Perhaps providing several values of the correlation coefficient for different ranges of quantiles could be useful. For example, if the correlation coefficient is close to 1 for the middle 97% of the data and much lower at the tails, this tells us the distribution of residuals is approximately normal, with some funniness going on in the tails.
Best to keep simple, and see if linear methods work "well enuff". You can judge your goodness of fit GENERALLY by looking at the R squared AND F statistic, together, never separate. Adding variables to your model that have no bearing on your dependant variable can increase R2, so you must also consider F statistic.
You should also compare your model to other nested, or more simpler, models. Do this using log liklihood ratio test, so long as dependant variables are the same.
Jarque–Bera test is good for testing the normality of the residual distribution.