I want to perform linear regression with interaction between 2 factors for 80 variables (human data, i.e., age, weight, height, hemoglobin etc.). I checked for normality of variables and more of them had failed shapiro.test.
Is it statistically correct to transform (log transform) and perform the test. or do I seperate them group-wise and try shapiro again?
Thank you
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I am rleatively new to statistics and am stuggling with the normality assumption.
I understand that parametric tests are underpinned by the assumption that the data is normally distributed, but there seems to be lots of papers and articles providing conflicting information.
Some articles say that independant variables need to be normally disrbiuted and this may require a transformation (log, SQRT etc.). Others says that in linear modelling there are no assumptions about any linear the distribution of the independent variables.
I am trying to create a multiple regression model to predict highest pain scores on hospital admissions:
DV: numeric pain scores (0-no pain -> 5 intense pain)(discrete- dependant variable).
IVs: age (continuous), weight (continuous), sex (nominal), depreviation status (ordinal), race (nominal).
Can someone help clear up the following for me?
Before fitting a model, do I need to check the whether my independant variables are normally distributed? If so, why? Does this only apply to continuous variables (e.g. age and weight in my model)?
If age is positively skewed, would a transformation (e.g. log, SQRT) be appropriate and why? Is it best to do this before or after fitting a model? I assume I am trying to get close to a linear relationship between my DV and IV.
As part of the SPSS outputs it provides plots of the standardised residuals against predicted values and also normal P-P plots of standardised residuals. Are these tests all that is needed to check the normality assumption after fitting a model?
Many Thanks in advance!
I'm using "Local Outlier Factor" for anomaly detection. The algorithm has a parameter called "contamination". This parameter represents the proportion of outliers. In my case, "0.0058" is the best value for the contamination parameter.
#parameters
n_neighbors = 750
p = 7
contamination = 0.0058 # the proportion of outliers
lof = LocalOutlierFactor(n_neighbors=n_neighbors, p=p, contamination=contamination)
y_pred_train = lof.fit_predict(data_scaled)
I found this value after trying many different values. However, I need to find the best value for contamination parameter without trying different values.
Here is the shape of the data:
I have two questions;
Is it possible to predict the best value of contamination parameter before executing the anomaly detection algorithm?
In real world applications, is it possible for an anomaly detection model to detect all anomalies perfectly?
Thanks in advance.
Local Outlier Factor value is a commonly used anomaly detection tool. It takes a local approach to better detect outliers about their neighbors, whereas a global strategy, might not be the best detection for datasets that fluctuate in density.
It totally depends on your dataset:
Do you have a tight, clean, and uniform dataset? Then a LOF value of 1.05 could be an outlier.
Do you have a sparse dataset, varying in density, with many local fluctuations specific to that local cluster? Then a LOF value of 2 could still be an inlier.
I have a particular classification problem that I was able to improve using Python's abs() function. I am still somewhat new when it comes to machine learning, and I wanted to know if what I am doing is actually "allowed," so to speak, for improving a regression problem. The following line describes my method:
lr = linear_model.LinearRegression()
predicted = abs(cross_val_predict(lr, features, labels_postop_IS, cv=10))
I attempted this solution because linear regression can sometimes produce negative predictions values, even though my particular case, these predictions should never be negative, as they are a physical quantity.
Using the abs() function, my predictions produce a better fit for the data.
Is this allowed?
Why would it not be "allowed". I mean if you want to make certain statistical statements (like a 95% CI e.g.) you need to be careful. However, most ML practitioners do not care too much about underlying statistical assumptions and just want a blackbox model that can be evaluated based on accuracy or some other performance metric. So basically everything is allowed in ML, you just have to be careful not to overfit. Maybe a more sensible solution to your problem would be to use a function that truncates at 0 like f(x) = x if x > 0 else 0. This way larger negative values don't suddenly become large positive ones.
On a side note, you should probably try some other models as well with more parameters like a SVR with a non-linear kernel. The thing is obviously that a LR fits a line, and if this line is not parallel to your x-axis (thinking in the single variable case) it will inevitably lead to negative values at some point on the line. That's one reason for why it is often advised not to use LRs for predictions outside the "fitted" data.
A straight line y=a+bx will predict negative y for some x unless a>0 and b=0. Using logarithmic scale seems natural solution to fix this.
In the case of linear regression, there is no restriction on your outputs.
If your data is non-negative (as in your case the values are physical quantities and cannot be negative), you could model using a generalized linear model (GLM) with a log link function. This is known as Poisson regression and is helpful for modeling discrete non-negative counts such as the problem you described. The Poisson distribution is parameterized by a single value λ, which describes both the expected value and the variance of the distribution.
I cannot say your approach is wrong but a better way is to go towards the above method.
This results in an approach that you are attempting to fit a linear model to the log of your observations.
I am currently modeling some data using a binary logistic regression. The dependent variable has a good number of positive cases and negative cases - it is not sparse. I also have a large training set (> 100,000) and the number of main effects I'm interested in is about 15 so I'm not worried about a p>n issue.
What I'm concerned about is that many of my predictor variables, if continuous, are zero most of the time, and if nominal, are null most of the time. When these sparse predictor variables take a value > 0 (or not null), I know because of familiarity with the data that they should be of importance in predicting my positive cases. I have been trying to look for information on how the sparseness of these predictors could be affecting my model.
In particular, I would not want the effect of a sparse but important variable to be not included in my model if there is another predictor variable that is not sparse and is correlated but actually doesn't do as good a job of predicting the positive cases. To illustrate an example, if I were trying to model whether or not someone ended up being accepted at a particular ivy league university and my three predictors were SAT score, GPA, and "donation > $1M" as a binary, I have reason to believe that "donation >$1M", when true, is going to be very predictive of acceptance - more so than a high GPA or SAT - but it is also very sparse. How, if at all, is this going to effect my logistic model and do I need to make adjustments for this? Also, would another type of model (say decision tree, random forest, etc) handle this better?
Thanks,
Christie
I have training data that falls into two classes, let's say Yes and No. The data represents three tasks, easy, medium and difficult. A person performs these tasks and is classified into one of the two classes as a result. Each task is classified independently and then the results are combined. I am using 3 independently trained SVM classifiers and then voting on the final result.
I am looking to provide a measure of confidence or probability associated with each classification. LIBSVM can provide a probability estimate along with the classification for each task (easy, medium and difficult, say Pe, Pm and Pd) but I am unsure of how best to combine these into an overall estimate for the final classification of the person (let's call it Pp).
My attempts so far have been along the lines of a simple average:
Pp = (Pe + Pm + Pd) / 3
An Inverse-variance weighted average (since each task is repeated a few times and sample variance (VARe, VARm and VARd) can be calculated - in which case Pe would be a simple average of all the easy samples):
Pp = (Pe/VARe + Pm/VARm + Pd/VARd) / (( 1/VARe ) + ( 1/VARm ) + ( 1/VARd ))
Or a multiplication (under the assumption that these events are independent, which I am unsure of since the underlying tasks are related):
Pp = Pe * Pm * Pd
The multiplication would provide a very low number, so it's unclear how to interpret that as an overall probability when the results of the voting are very clear.
Would any of these three options be the best or is there some other method / detail I'm overlooking?
Based on your comment, I will make the following suggestion. If you need to do this as an SVM (and because, as you say, you get better performance when you do it this way), take the output from your intermediate classifiers and feed them as features to your final classifier. Even better, switch to a multi-layer Neural Net where your inputs represent inputs to the intermediates, the (first) hidden layer represents outputs to the intermediate problem, and subsequent layer(s) represent the final decision you want. This way you get the benefit of an intermediate layer, but its output is optimised to help with the final prediction rather than for accuracy in its own right (which I assume you don't really care about).
The correct generative model for these tests likely looks something like the following:
Generate an intelligence/competence score i
For each test t: generate pass/fail according to p_t(pass | i)
This is simplified, but I think it should illustrate tht you have a latent variable i on which these tests depend (and there's also structure between them, since presumably p_easy(pass|i) > p_medium(pass|i) > p_hard(pass|i); you could potentially model this as a logistic regression with a continuous 'hardness' feature). I suspect what you're asking about is a way to do inference on some thresholding function of i, but you want to do it in a classification way rather than as a probabilistic model. That's fine, but without explicitly encoding the latent variable and the structure between the tests it's going to be hard (and no average of the probabilities will account for the missing structure).
I hope that helps---if I've made assumptions that aren't justified, please feel free to correct.