How do I classify variables in R when the classifying output is known only for a group of variables? Think of this as being similar to the 'Mastermind' board game.
Or, here is a concrete example I'm working on: a person eats different types of food on different days, and she either has an allergic reaction (to something she ate that day), or she does not. These data are available for a number of days. What is the person allergic to?
With real data, you cannot do simple elimination (all foods she ate on days with no reaction are fine), because there will be false positives and false negatives in the data. A probabilistic approach is needed (99% allergic to spinach, 20% allergic to mint, etc.).
This is really more of a Statistics 101 question and thus better suited for stats.stackexchange.com but I will handle it.
The answer to your food analogy example is to use something like
lm() # for linear models (least squares), univariate or multivariate
glm() # generalized linear models (note: despite the name you can use these 2 for non-linear models as well, like polynomial regression)
nnet #basic neural networks and
randomForest()
the package caret has over 100 classification models
and etc, etc. There are hundreds if not thousands of probabilistic approaches you could take. You can use normal equations, gradient descent, etc, etc. The possibilities are practically endless.
This should get you started:
https://cran.r-project.org/web/views/MachineLearning.html
https://cran.r-project.org/web/views/Multivariate.html
http://blog.revolutionanalytics.com/2012/08/cheat-sheet-for-prediction-and-classification-models-in-r.html
I'm sorry but I've never heard of 'Mastermind'.
Related
As said above I'm trying to create a model for detecting spam emails based on word occurrences. my information from my dataset is as follows:
about 2800 variables representing each word and the frequency of their occurrences
binary spam variable 1 for spam 0 for legit
I've been using online resources but can only find logistic regression and NN tutorials for much smaller datasets, which seem much simpler in comparison. So far I've totaled up the total words for spam and non spam to analyze, but I'm having trouble creating the model itself
Does anyone have any sources or insight on how to manage this with a much larger dataset?
Apologies for the simple question (if it is so) I appreciate any advice.
A classical approach uses a generalised linear model (GLM) with a penalty for the number of variables. The GLM will be the logistic regression model in this case. The classic approach for the penalty is the LASSO, ridge regression and elastic net techniques. The shrinkage in your parameter values may be such that no parameters are selected to be predictive if your ratio of the number of variables (p) to the number of samples (N) is too high. Some parameters can control the shrinkage for that. It's overall a well studied topic. Your questions haven't asked about the programming language you will use, but you may find helpful packages in Python, R, Julia and other widespread data science programming languages. There will also be a lot of information in the CV community.
I would start analysing each variable individually. I would implement a logistic regression for each one, and remain only with those whose p-value is really significative.
After this first step, then you can run a more complex logistic regression model, where you include the remaining variables in the first step.
I am trying to build a Mixed Model Lasso model using glmmLasso in RStudio. However, I am looking for some assistance.
I have the equation of my model as follows:
glmmModel <- glmmLasso(outcome ~ year + married ,list(ID=~1), lambda = 100, family=gaussian(link="identity"), data=data1,control = list(print.iter=TRUE))
where outcome is a continuous variable, year is the year the data was collected, and married is a binary indicator (1/0) of whether or not the subject is married. I eventually would like to include more covariates in my model, but for the purpose of successfully first getting this to run, right now I am just attempting to run a model with these two covariates. My data1 dataframe is 48000 observations and 57 variables.
When I click run, however, the model runs for many hours (48+) without stopping. The only feedback I am getting is "ITERATION 1," "ITERATION 2," etc... Is there something I am missing or doing wrong? Please note, I am running on a machine with only 8 GB RAM, but I don't think this should be the issue, right? My dataset (48000 observations) isn't particularly large (at least I don't think so). Any advice or thoughts would be appreciated on how I can fix this issue. Thank you!
This is too long to be a comment, but I feel like you deserve an answer to this confusion.
It is not uncommon to experience "slow" performance. In fact in many glmm implementations it is more common than not. The fact is that Generalized Linear Mixed Effect models are very hard to estimate. For purely gaussian models (no penalizer) a series of proofs gives us the REML estimator, which can be estimated very efficiently, but for generalized models this is not the case. As such note that the Random Effect model matrix can become absolutely massive. Remember that for every random effect, you obtain a block-diagonal matrix so even for small sized data, you might have a model matrix with 2000+ columns, that needs to go through optimization through PIRLS (inversions and so on).
Some packages (glmmTMB, lme4 and to some extend nlme) have very efficient implementations that abuse the block-diagonality of the random effect matrix and high-performance C/C++ libraries to perform optimized sparse-matrix calculations, while the glmmLasso (link to source) package uses R-base to perform all of it's computations. No matter how we go about it, the fact that it does not abuse sparse computations and implements it's code in R, causes it to be slow.
As a side-note, my thesis project had about 24000~ observations, with 3 random effect variables (and some odd 20 fixed effects). The fitting process of this dataset could take anywhere between 15 minutes to 3 hours, depending on the complexity, and was primarily decided by the random effect structure.
So the answer from here:
Yes glmmLasso will be slow. It may take hours, days or even weeks depending on your dataset. I would suggest using a stratified (or/and clustered) subsample across independent groups, fit the model using a smaller dataset (3000 - 4000 maybe?), to obtain initial starting points, and "hope" that these are close to the real values. Be patient. If you think neural networks are complex, welcome to the world of generalized mixed effect models.
I want to explore the following variables and their 2-way interactions as possible predictors: the number of siblings (nsibs), weaning age (wmonth), maternal age (mthage), race, poverty, birthweight (bweight) and maternal smoking (smoke).
I created my Cox regression formula but I don't know how to form the 2-way interaction with the predictors:
coxph(Surv(wmonth,chldage1)~as.factor(nsibs)+mthage+race+poverty+bweight+smoke,data=pneumon)
final<-step(coxph(Surv(wmonth,chldage1)~(as.factor(nsibs)+mthage+race+poverty+bweight+smoke)^2,data=pneumon),direction='backward')
The formula interface is the same for coxph as it is for lm or glm. If you need to form all the two-way interactions, you use the ^-operator with a first argument of the "sum" of the covariates and a second argument of 2:
coxph(Surv(wmonth,chldage1) ~
( as.factor(nsibs)+mthage+race+poverty+bweight+smoke)^2,
data=pneumon)
I do not think there is a Cox regression step stepdown function. Thereau has spoken out in the past against making the process easy to automate. As Roland notes in his comment the prevailing opinion among all the R Core package authors is that stepwise procedures are statistically suspect. (This often creates some culture shock when persons cross-over to R from SPSS or SAS, where the culture is more accepting of stepwise procedures and where social science stats courses seem to endorse the method.)
First off you need to address the question of whether your data has enough events to support such a complex model. The statistical power of Cox models is driven by the number of events, not the number of subjects at risk. An admittedly imperfect rule of thumb is that you need 10-15 events for each covariate and by expanding the interactions perhaps 10-fold, you expand the required number of events by a similar factor.
Harrell has discussed such matters in his RMS book and rms-package documentation and advocates applying shrinkage to the covariate estimates in the process of any selection method. That would be a more statistically principled route to follow.
If you do have such a large dataset and there is no theory in your domain of investigation regarding which covariate interactions are more likely to be important, an alternate would be to examine the full interaction model and then proceed with the perspective that each modification of your model adds to the number of degrees of freedom for the overall process. I have faced such a situation in the past (thousands of events, millions at risk) and my approach was to keep the interactions that met a more stringent statistical theory. I restricted this approach to groups of variables that were considered related. I examined them first for their 2-way correlations. With no categorical variables in my model except smoking and gender and 5 continuous covariates, I kept 2-way interactions that had delta-deviance (distributed as chi-square stats) measures of 30 or more. I was thereby retaining interactions that "achieved significance" where the implicit degrees of freedom were much higher than the naive software listings. I also compared the results for the retained covariate interactions with and without the removed interactions to make sure that the process had not meaningfully shifted the magnitudes of the predicted effects. I also used Harrell's rms-package's validation and calibration procedures.
I am working in machine learning. I am stuck in one of the thing.
I want to compare 4 machine learning techniques among 10 datasets. After performing experiment i got Area Under Curve value. After this i have applied Analysis of variance test which shows there is a significant difference between 4 machine learning techniques.
Now my problem is that which test will conclude that particular algorithm perform well compared to other algorithm and i want only one winner among the machine learning techniques.
A classifier's quality can be measured by the F-Score which measures the test's accuracy. Comparing these respective scores will give you a simple measure.
However, if you want to measure whether the difference between the classifiers' accuracies is significant, you can try the Bayesian Test or, if classifiers are trained once, McNemar's test.
There are other possibilities and the papers On Comparing Classifiers: Pitfalls to Avoid and a
Recommended Approach and Approximate Statistical Tests for Comparing
Supervised Classification Learning Algorithms are probably worth reading.
If you are gathering performance metrics (ROC,accuracy,sensitivity,specificity...) from identicially resampled data sets then you can perform statistical tests using paired comparisons. Most statistical software impliment Tukeys Range test (ANOVA). https://en.wikipedia.org/wiki/Tukey%27s_range_test. A formal treatment of this material is here: http://epub.ub.uni-muenchen.de/4134/1/tr030.pdf. This is the test I like to use for the purpose you discuss, although there are others and people have varying opinions.
You will still have to choose how you will sample based on your data (k-fold), repeated (k-fold), bootstrap, leave one out, repeated training test splits. Bootstrap methods tend to give you the tightest confidence intervals after leave one out; but leave one out might not be an option if your data is huge.
That being said you may also need to consider the problem domain. False positives may be an issue in classification. You may need to consider other metrics to choose the best performer for the domain. AUC might not always be the best model for a specific domain. For instance a credit card company may not want to deny a transaction to customers, we need a very low false positive on fraud classification.
You may also want to consider implementation. If a logistic regression performs near as well it may be a better choice over a more complicated implementation of a random forest. Are there legal implications to model use (Fair Credit Reporting Act...)?
A common sense approach is to begin with something like RF or Gradient boosted trees to get an empirical sense of a performance ceiling. Then build simpler models and use the simpler model that performs reasonabley well compared to the ceiling.
Or you could combine all your models using something like LASSO... or some other model.
I have a few hundred thousand measurements where the dependent
variable is a probability, and would like to use logistic regression.
However, the covariates I have are all categorical, and worse, are all
nested. By this I mean that if a certain measurement has "city -
Phoenix" then obviously it is certain to have "state - Arizona" and
"country - U.S." I have four such factors - the most granular has
some 20k levels, but if need be I could do without that one, I think.
I also have a few non-nested categorical covariates (only four or so,
with maybe three different levels each).
What I am most interested in
is prediction - given a new observation in some city, I would like to
know the relevant probability/dependent variable. I am not interested
as much in the related inferential machinery - standard deviations,
etc - at least as of now. I am hoping I can afford to be sloppy.
However, I would love to have that information unless it requires
methods that are more computationally expensive.
Does anyone have any advice on how to attack this? I have looked into
mixed effects, but am not sure it is what I am looking for.
I think this is more of model design question than on R specifically; as such, I'd like to address the context of the question first then the appropriate R packages.
If your dependent variable is a probability, e.g., $y\in[0,1]$, a logistic regression is not data appropriate---particularly given that you are interested in predicting probabilities out of sample. The logistic is going to be modeling the contribution of the independent variables to the probability that your dependent variable flips from a zero to a one, and since your variable is continuous and truncated you need a different specification.
I think your latter intuition about mixed effects is a good one. Since your observations are nested, i.e., US <-> AZ <-> Phoenix, a multi-level model, or in this case a hierarchical linear model, may be the best specification for your data. The best R packages for this type of modeling are multilevel and nlme, and there is an excellent introduction to both multi-level models in R and nlme available here. You may be particularly interested in the discussion of data manipulation for multi-level modeling, which begins on page 26.
I would suggest looking into penalised regressions like the elastic net. The elastic net is used in text mining where each column represents the present or absence of a single word, and there maybe hundreds of thousands of variables, an analogous problem to yours. A good place to start with R would be the glmnet package and its accompanying JSS paper: http://www.jstatsoft.org/v33/i01/.