I am applying a causal method to a cohort study analysis on pollutant exposure and disease X. Based on our understanding of the disease, we believe that aging is the only confounder.
From what I understand, age would be the item in our minimally sufficient set required to evaluate the outcome/exposure relationship.
Assuming all other causal assumptions are met, does the minimally sufficient set represent the only variable that should be included in the model outside of the exposure?
Could I still include covariates like smoking history and gender that effect the outcome versus age which effects the outcome and the exposure?
Please help! I can’t seem to find anything conclusive online. I want to include the other covariates because I feel their effect sizes contextualize the effect of the exposure.
Yes, you can add additional variables to your analysis. They will either be good, neutral, or bad, depending on the causal structure of your problem.
I strongly recommend the paper A Crash Course in Good and Bad Controls by Cinelli, Forney, and Pearl, for a comprehensive classification of possible cases.
Your description of gender and smoking status affecting only the outcome seems to comply with model 8 in the paper. These are, in general, good variables to add, since they will help explaining the variance of the outcome, therefore reducing the variance left for the treatment to explain - practically increasing the precision of the treatment effect estimation.
Related
I'm working on a simple project in which I'm trying to describe the relationship between two positively correlated variables and determine if that relationship is changing over time, and if so, to what degree. I feel like this is something people probably do pretty often, but maybe I'm just not using the correct terminology because google isn't helping me very much.
I've plotted the variables on a scatter plot and know how to determine the correlation coefficient and plot a linear regression. I thought this may be a good first step because the linear regression tells me what I can expect y to be for a given x value. This means I can quantify how "far away" each data point is from the regression line (I think this is called the squared error?). Now I'd like to see what the error looks like for each data point over time. For example, if I have 100 data points and the most recent 20 are much farther away from where the regression line/function says it should be, maybe I could say that the relationship between the variables is showing signs of changing? Does that make any sense at all or am I way off base?
I have a suspicion that there is a much simpler way to do this and/or that I'm going about it in the wrong way. I'd appreciate any guidance you can offer!
I can suggest two strands of literature that study changing relationships over time. Typing these names into google should provide you with a large number of references so I'll stick to more concise descriptions.
(1) Structural break modelling. As the name suggest, this assumes that there has been a sudden change in parameters (e.g. a correlation coefficient). This is applicable if there has been a policy change, change in measurement device, etc. The estimation approach is indeed very close to the procedure you suggest. Namely, you would estimate the squared error (or some other measure of fit) on the full sample and the two sub-samples (before and after break). If the gains in fit are large when dividing the sample, then you would favour the model with the break and use different coefficients before and after the structural change.
(2) Time-varying coefficient models. This approach is more subtle as coefficients will now evolve more slowly over time. These changes can originate from the time evolution of some observed variables or they can be modeled through some unobserved latent process. In the latter case the estimation typically involves the use of state-space models (and thus the Kalman filter or some more advanced filtering techniques).
I hope this helps!
What are the tips & tricks to improve our auc_roc_score?
Example:
Is balanced data required?
Is recall is more important than precision?
Is oversampling is usually better than undersampling?
Thanks again!
This is highly dependent upon the type of data in use and the type of model it is trained on along with the hyper parameters being currently used. The ROC is just the outcome of how well the data pre processing and model building is done. Thus you must look into ways of improving your model. Also precision and recall are useful in their own ways. It depends on the scenario.
Like precision answers the question :
What proportions of the predicted True labels were actually correct ?
whereas recall answers :
What proportion of the actually correct labels were identified correctly ?
Thus you would want a higher recall in case of identifying a corona patient while you would prefer a higher precision when it comes to the fact that the cost of acting is high and the cost of not acting is low.
Also, what exactly do u mean by balanced data varies from situation to situation.
Thus if you could specify the kind of model, problem and data in use, we may be able to help you more.
Please share the code of your model for the same.
I am trying to generate a model that uses several physico-chemical properties of a molecule (incl. number of atoms, number of rings, volume, etc.) to predict a numeric value Y. I would like to use PLS Regression, and I understand that standardization is very important here. I am programming in Python, using scikit-learn. The type and range for the features varies. Some are int64 while other are float. Some features generally have small (positive or negative) values, while other have very large value. I have tried using various scalers (e.g. standard scaler, normalize, minmax scaler, etc.). Yet, the R2/Q2 are still low. I have a few questions:
Is it possible that by scaling, some of the very important features lose their significance, and thus contribute less to explaining the variance of the response variable?
If yes, if I identify some important features (by expert knowledge), is it OK to scale other features but those? Or scale the important features only?
Some of the features, although not always correlated, have values that are in a similar range (e.g. 100-400), compared to others (e.g. -1 to 10). Is it possible to scale only a specific group of features that are within the same range?
The whole idea of scaling is to make models more robust to analysis on features space. For example, if you have 2 features as 5 Kg and 5000 gm, we know both are same, but for some algorithm, which are sensitive to metric space such as KNN, PCA etc, they will be more weighted towards second features, so scaling must be done for these algos.
Now coming to your question,
Scaling doesn't effect the significance of features. As i explained above, it helps in better analysis of data.
No, you should not do, reason explained above.
If you want to include domain knowledge in your model, you can use it as prior information. In short, for linear model, this is same as regularization. It has very good features. if you think, you have many useless-features, you can use L1 regularization, which creates sparse effect on features space, which is nothing but assign 0 weight to useless features. Here is the link for more-info.
One more point, some method such as tree based model doesn't need scaling, In last, it mostly depend on the model, you choose.
Lose significance? Yes. Contribute less? No.
No, it's not OK. It's either all or nothing.
No. The idea of scaling is not to decrease / increase significance / effect of a variable. It's to transform all variables to a common scale that can be interpreted.
Running a survival analysis, assume the p-value regarding a variable is statistically significant - let's say with a positive association with the outcome. However, according to the Schoenfeld residuals, the proportional hazard (PH) assumption has is violated.
Which scenario among below could possibly happen after correcting for PH violations?
The p-value may not be significant anymore.
p-value still significant, but the size of HR may change.
p-value still significant, but the direction of association may be altered (i. e. a positive association may end up being negative).
The PH assumption violation usually means that there is an interaction effect that needs to be included in the model. In the simple linear regression, including a new variable may alter the direction of the existing variables' coefficients due to the collinearity. Can we use the same rationale in the case above?
Therneau and Gramsch have written a very useful text, "Modeling Survival Data" that has an entire chapter on testing proportionality. At the end of the chapter is a section on causes and modeling alternatives, which I think can be used for answering this question. Since you mention interactions it makes your question about a particular p-value rather ambiguous and vague.
1) Certainly if you have chosen a particular measurement as the subject of your interest and it turns out the all of the effects are due to its interaction with another variable that you happened to also measure, then you may be in a position where the variable-of-interest's p-value will decrease, possibly to zero.
2) It's almost certain that modification of a model with a different structure (say will the addition of time-varying covariates or a different treatment of time) will result in a different estimated HR for a particular covariate and I think it would be impossible to predict the direction of the change.
3) As to whether to sign of the coefficient could change, I'm quite sure that would be possible as well. The scenario I'm thinking of would have a mixture of two groups say men and women and one of the groups had a sub-group whose early mortality was greatly increased, e.g. breast cancer, while the surviving members of that group would have a more favorable survival expectation. The base model might show a positive coefficient (high risk) while a model that was capable of identifying the subgroup at risk would then allow the gender-related coefficient to become negative (lower risk).
I want to use machine learning to identify the signature of a user who converts to a subscriber of a website given their behavior over time.
Let's say my website has 6 different features which can be used before subscribing and users can convert to a subscriber at any time.
For a given user I have stats which represent the intensity on a continuous range of that user's interaction with features 1-6 on a daily basis so:
D1: f1,f2,f3,f4,f5,f6
D2: f1,f2,f3,f4,f5,f6
D3: f1,f2,f3,f4,f5,f6
D4: f1,f2,f3,f4,f5,f6
Let's say on day 5, the user converts.
What machine using algorithms would help me identify which are the most common patterns in feature usage which lead to a conversion?
(I know this is a super basic classification question, but I couldn't find a good example using longitudinal data, where input vectors are ordered by time like I have)
To develop the problem further, let's assume that each feature has 3 intensities at which the user can interact (H, M, L).
We can then represent each user as a string of states of interaction intensity. So, for a user:
LLLLMM LLMMHH LLHHHH
Would mean on day one they only interacted significantly with features 5 and 6, but by the third day they were interacting highly with features 3 through 6.
N-gram Style
I could make these states words and the lifetime of a user a sentence. (Would probably need to add a "conversion" word to the vocabulary as well)
If I ran these "sentences" through an n-gram model, I could get the likely future state of a user given his/her past few state which is somewhat interesting. But, what I really want to know the most common sets of n-grams that lead to the conversion word. Rather than feeding in an n-gram and getting the next predicted word, I want to give the predicted word and get back the 10 most common n-grams (from my data) which would be likely to lead to the word.
Amaç Herdağdelen suggests identifying n-grams to practical n and then counting how many n-gram states each user has. Then correlating with conversion data (I guess no conversion word in this example). My concern is that there would be too many n-grams to make this method practical. (if each state has 729 possibilities, and we're using trigrams, thats a lot of possible trigrams!)
Alternatively, could I just go thru the data logging the n-grams which led to the conversion word and then run some type of clustering on them to see what the common paths are to a conversion?
Survival Style
Suggested by Iterator, I understand the analogy to a survival problem, but the literature here seems to focus on predicting time to death as opposed to the common sequence of events which leads to death. Further, when looking up the Cox Proportional Hazard model, I found that it does not event accommodate variables which change over time (its good for differentiating between static attributes like gender and ethnicity)- so it seems very much geared toward a different question than mine.
Decision Tree Style
This seems promising though I can't completely wrap my mind around how to structure the data. Since the data is not flat, is the tree modeling the chance of moving from one state to another down the line and when it leads to conversion or not? This is very different than the decision tree data literature I've been able to find.
Also, need clarity on how to identify patterns which lead to conversion instead a models predicts likely hood of conversion after a given sequence.
Theoretically, hidden markov models may be a suitable solution to your problem. The features on your site would constitute the alphabet, and you can use the sequence of interactions as positive or negative instances depending on whether a user finally subscribed or not. I don't have a guess about what the number of hidden states should be, but finding a suitable value for that parameter is part of the problem, after all.
As a side note, positive instances are trivial to identify, but the fact that a user has not subscribed so far doesn't necessarily mean s/he won't. You might consider to limit your data to sufficiently old users.
I would also consider converting the data to fixed-length vectors and apply conceptually simpler models that could give you some intuition about what's going on. You could use n-grams (consecutive interaction sequences of length n).
As an example, assuming that the interaction sequence of a given user ise "f1,f3,f5", "f1,f3,f5" would constitute a 3-gram (trigram). Similarly, for the same user and the same interaction sequence you would have "f1,f3" and "f3,f5" as the 2-grams (bigrams). In order to represent each user as a vector, you would identify all n-grams up to a practical n, and count how many times the user employed a given n-gram. Each column in the vector would represent the number of times a given n-gram is observed for a given user.
Then -- probably with the help of some suitable normalization techniques such as pointwise mutual information or tf-idf -- you could look at the correlation between the n-grams and the final outcome to get a sense of what's going on, carry out feature selection to find the most prominent sequences that users are involved in, or apply classification methods such as nearest neighbor, support machine or naive Bayes to build a predictive model.
This is rather like a survival analysis problem: over time the user will convert or will may drop out of the population, or will continue to appear in the data and not (yet) fall into neither camp. For that, you may find the Cox proportional hazards model useful.
If you wish to pursue things from a different angle, namely one more from the graphical models perspective, then a Kalman Filter may be more appealing. It is a generalization of HMMs, suggested by #AmaçHerdağdelen, which work for continuous spaces.
For ease of implementation, I'd recommend the survival approach. It is the easiest to analyze, describe, and improve. After you have a firm handle on the data, feel free to drop in other methods.
Other than Markov chains, I would suggest decision trees or Bayesian networks. Both of these would give you a likely hood of a user converting after a sequence.
I forgot to mention this earlier. You may also want to take a look at the Google PageRank algorithm. It would help you account for the user completely disappearing [not subscribing]. The results of that would help you to encourage certain features to be used. [Because they're more likely to give you a sale]
I think Ngramm is most promising approach, because all sequnce in data mining are treated as elements depndent on few basic steps(HMM, CRF, ACRF, Markov Fields) So I will try to use classifier based on 1-grams and 2 -grams.