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I'm not sure if this is a question for stackoverflow, or crossvalidated.
I'm looking for away to include covariate measures when calculating the correlation between two measures. For example, Lets say I have 100 samples, for which I have two measurements, x and y. Now lets say I also have a third measure, a covariate (lets say age). I want to measure the correlation between x and y, but I also want to ignore any of that correlation that comes from the covariate, age.
If I'm fitting a linear model, I could simply add the term to the model:
lm(y~x+age)
I know you can't calculate correlation with this kind of model in R (using ~).
So I want to know:
Does what I'm asking even make sense to do? I suspect it may not.
If it does, what R packages should I be using?
It sounds like you're asking for a semipartial correlation. You want the correlation between x and y partialling out the correlation between x and z. You need to read about partial and semipartial correlations.
The ppcor package in R will then help you with the calculations.
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I have set of customers with different attributes continuous, categorical, binary and ordinal.
How can I cluster them knowing that we cannot apply the same distance metrics on the these different types of attributes?
Thank you in advance
As mentioned already daisy package is an option which does an automatic selection of best distance metric based on data type.But I would suggest the following approach and request expert to please chime in.
Rather than automatic selection identify and remove some correlated variables like(some examples)
Pearson Correlation: for continuous variable
Chi Square Test: for categorical variables
Categorical vs Numerical: One way Anova test etc.
Taking the subset of useful variables consider doing One-Hot Encoding of categorical variables and maybe convert ordinal to continuous (or categorical and one-hot encode). Test using different distance metric like Euclidean, Manhattan etc to evaluate the result. You will get a better clarity of the overall clustering process in this way.
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My current linear model is: fit<-lm(ES~Area+Anear+Dist+DistSC+Elevation)
I have been asked to further this by:
Fit a linear model for ES using the five explanatory variables and
include up to quadratic terms and first order interactions (i.e. allow
Area^2 and Area*Elevation, but don't allow Area^3 or
Area*Elevation*Dist).
From my research I can do +I(Area^2) and +(Area*Elevation) but this would make a huge list.
Assuming I am understanding the question correctly I would be adding 5 squared terms and 10 * terms giving 20 total. Or do I not need all of these?
Is that really the most efficient way of going about it?
EDIT:
Note that I am planning on carrying out a stepwise regression for the null model and the full model after. I am seemingly having trouble with this when using poly.
Look at ?formula to further your education:
fit<-lm( ES~ (Area+Anear+Dist+DistSC+Elevation)^2 )
Those will not be squared terms but rather part of what you were asked to provide... all the 2-way interactions (and main effects). Formula "mathematics" is different than regular use of powers. To add the squared terms in a manner that allows proper statistical interpretation use poly
fit<-lm( ES~ (Area+Anear+Dist+DistSC+Elevation)^2 +
poly(Area,2) +poly(Anear,2)+ poly(Dist,2)+ poly(DistSC,2)+ poly(Elevation,2) )
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http://i43.tinypic.com/8yz893.png
The figure in the link shows the relation between one of my predictors(vms) and the response(responses[i]).
We can distinguish many log-like trends within the same graph.
According to this, a single value of my predictor can be mapped to many values of the response.
Is this acceptable or should I be alarmed that there is a problem with my data?
What regression model would seem more suitable for this picture?
This isn't really an R question, but rather a general statistics question, so you may get downvoted, but I'll try to help you out.
There's nothing wrong with having individual values of the predictor mapping to multiple values of response. This would be a problem if you were defining and evaluating a function, but you're not technically evaluating a function, you're evaluating the statistical relationship between two variables. You will then create a functional form to model this relationship.
It seems to me that a conventional OLS model would be very inappropriate here, as one of the assumptions of OLS is that the relationship between the predictor and the outcome variable is linear, which is clearly is not in this case. The relationship actually looks a lot like a 1/x curve, so you may want to try a 1/x transformation and see where that gets you.
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I have two multiple linear regression models, built using the same groups of subjects, variables, the only difference is the time point: one is baseline data and the other is obtained some time after.
I want to compare if there is any statistical significance between the two models. I have seen articles saying that using AIC maybe a better option over p-value when comparing models.
My question is: does it make sense to just purely compare the AIC using extractAIC in R, or to obtain the anova(lm)?
It is not standard to test for statistical significance between observations recorded at two points in time by estimating two different models.
You may mean that you are testing to see whether the observations recorded at a second point in time are statistically different from the first, by including some dummy variables, and testing the coefficients on these. Still, this is only estimating one model.
In your model you will have dummy variables for your second point in time, either one intercept or an intercept and an interaction dummy like this.
Then you should do both - test the p-value significance for either or both gammas in the models described, and also look at the AIC. There is no definitive 'better', as the articles likely described.
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I am running simple linear models(Y~X) in R where my predictor is a categorical variable (0-10). However, this variable is not normally distributed and none of the transformation techniques available are healpful (e.g. log, sq etc.) as the data is not negatively/positively skewed but rather all over the place. I am aware that for lm the outcome variable (Y) has to be normally distributed but is this also required for predictors? If yes, any suggestions of how to do this would be more than welcome.
Also, as the data I am looking at has two groups, patients vs controls (I am interested in group differences, as you can guess), do I have to look at whether the data is normally distributed within the two groups or overall across the two groups?
Thanks.
See #Roman LuĊĦtriks comment above: it does not matter how your predictors are distributed. (Except for problems with multicollinearity.) What is important is that the residuals be normal (and with homogeneous variances).