I have very little programming experience, but I'm working on a statistics project and would like to generate an unequal probability sample where the inclusion probability of a unit is based on its size (PPS).
Basically, I have two datasets:
ds1 lists US states and the parameter I'm trying to estimate
ds2 has the population size of each state.
My questions:
I want to use R to select a random sample from the first dataset using inclusion probabilities based on the population of each state (second dataset).
Also is there any way to use R to calculate these Generalized Unequal Probability Estimator formulas?
Also just a note on the formulas: pi_i is inclusion probability and pi_ij is joint inclusion probability.
There is a package for the same in R - pps and the documentation is here.
Also, there is another package called survey with a bit of documentation here.
I'm not sure of the difference between the two and haven't used them myself. Hope this is what you're looking for.
Yes, that's called weighted sampling. Simply set the weight to the size of the state, strictly you don't even need to normalize them by 1/sum(sizes) although it's always good practice to. There are tons of duplicate posts on SO showing how to do weighted sampling.
The only tiny complication is that you need to do a join() of the datasets ds1, ds2. Show us what code you've tried if it's causing problems. Recommend you use either dplyr or data.table.
Your second question should be asked as a separate question, and is offtopic on SO, or at least won't get a great response - best to ask statistical questions at sister site CrossValidated
Related
I am running an analysis of variances on a large distance matrix using adonis2 as described here: https://www.rdocumentation.org/packages/vegan/versions/2.4-2/topics/adonis
That method is frequently used in microbiome analysis to calculate beta diversity. That's also what I would like to do, i.e. to find out whether my community composition differs in response to an environmental variable (continuous)
Permanova returns one p value and there is no "official" post hoc test yet. That's where my question comes in:
I've come across publications saying they adjusted their permanova result using FDR/BH method. I cannot wrap my head around this. I'm confident I understand how FDR correction is calculated, I just don't see how that would be done for PERMANOVA, or, even more, how I would code it.
Can anyone help me out here?
Would be clearer if you provide an example of so-called publication. You are right that for each variable, permanova returns 1 p-value. However, if the model includes many variables, you would have 1 p-value for each variable and you need to correct for FDR.
For example in this publication looking at variation in gut microbiome, they wrote:
To calculate the variation explained by each of our collected host
factors, we performed an Adonis test implemented in QIIME. Each host
factor was calculated according to its explanation rate, and P values
were generated based on 1,000 permutations. All P values were then
adjusted using the Benjamini–Hochberg method.
You can also see an example of this in Table S2, I attached a screenshot here:
As you might be able to tell from the sample of my dataset, it contains a lot of dependency, with each study providing multiple outcomes for the construct I am looking at. I was planning on using the metacor library because I only have information about the sample size but not variance. However, all methods I came across to that deal with dependency such as the package rubometa use variance (I know some people average the effect size for the study but I read that tends to produce larger error rates). Do you know if there is an equivalent package that uses only sample size or is it mathematically impossible to determine the weights without it?
Please note that I am a student, no expert.
You could use the escalc function of the metafor package to calculate variances for each effect size. In the case of correlations, it only needs the raw correlation coefficients and the corresponding sample sizes.
See section "Outcome Measures for Variable Association" # https://www.rdocumentation.org/packages/metafor/versions/2.1-0/topics/escalc
I´ve a question regarding k-means clustering. We have a dataset with 120,000 observations and need to compute a k-means cluster solution with R. The problem is that k-means usually use Euclidean Distance. Our dataset consists of 3 continous variables, 11 ordinal (Likert 0-5) (i think it would be okay to handle them like continous) and 5 binary variables. Do you have any suggestion for a distance measure that we can use for our k-means approach with regards to the "large" dataset? We stick to k-means, so I really hope one of you has a good idea.
Cheers,
Martin
One approach would be to normalize the features and then just use the 11-dimensional
Euclidean Distance. Cast the binary values to 0/1 (Well, it's R, so it does that anyway) and go from there.
I don't see an immediate problem with this method other than k-means in 11 dimensions will definitely be hard to interpret. You could try to use a dimensionality reduction technique and hopefully make the k-means output easier to read, but you know way more about the data set than we ever could, so our ability to help you is limited.
You can certainly encode there binary variables as 0,1 too.
It is a best practise in statistics to not treat likert scale variables as numeric, because of that uneven distribution.
But I don't you will get meaningful k-means clusters. That algorithm is all about computing means. That makes sense on continuous variables. Discrete variables usually lack "resolution" for this to work well. Three mean then degrades to a "frequency" and then the data should be handled very differently.
Do not choose the problem by the hammer. Maybe your data is not a nail; and even if you'd like to make it with kmeans, it won't solve your problem... Instead, formulate your problem, then choose the right tool. So given your data, what is a good cluster? Until you have an equation that measures this, handing the data won't solve anything.
Encoding the variables to binary will not solve the underlying problem. Rather, it will only aid in increasing the data dimensionality, an added burden. It's best practice in statistics to not alter the original data to any other form like continuous to categorical or vice versa. However, if you are doing so, i.e. the data conversion then it must be in sync with the question to solve as well as you must provide valid justification.
Continuing further, as others have stated, try to reduce the dimensionality of the dataset first. Check for issues like, missing values, outliers, zero variance, principal component analysis (continuous variables), correspondence analysis (for categorical variables) etc. This can help you reduce the dimensionality. After all, data preprocessing tasks constitute 80% of analysis.
Regarding the distance measure for mixed data type, you do understand the mean in k will work only for continuous variable. So, I do not understand the logic of using the algorithm k-means for mixed datatypes?
Consider choosing other algorithm like k-modes. k-modes is an extension of k-means. Instead of distances it uses dissimilarities (that is, quantification of the total mismatches between two objects: the smaller this number, the more similar the two objects). And instead of means, it uses modes. A mode is a vector of elements that minimizes the dissimilarities between the vector itself and each object of the data.
Mixture models can be used to cluster mixed data.
You can use the R package VarSelLCM which models, within each cluster, the continuous variables by Gaussian distributions and the ordinal/binary variables.
Moreover, missing values can be managed by the model at hand.
A tutorial is available at: http://varsellcm.r-forge.r-project.org/
I have a question about LASSO. I'm getting crazy because it is something that I can not solve only according to my background. I'm a biologist.
Briefly I run LASSO using the R library "penalized". In particular I used the opt1D function with around 500 simulations on a data.frame (numerical) of around 30 columns that are my biomarkers (gene expression). I want to test and 3000 rows that are people of which around 50 are tumours and all the others are normals.
Unfortunately by using L1 regularization, all and really all coefficients of 500 simulations are 0. If I check L2 matrix of coefficients they are close to 0. Now my point is that I cannot think that all my biomarkers are not able to distinguish between Normals and Tumors.
I don't know if what I have done is all I can to check for the discriminatory potential of my molecules. Is there something else I can do to understand why are they all 0 and also is there something else I can do to verify that really they are not able to stratify my cohort?
Did you consider fitting your data without penalization before using regularization? L1 regularization will naturally result in a significant number of zero coefficients.
As a side note I would first run PCA/PCoA and see whether or not your genes separate according to your class variable. This could save you some time and allow you to trim your data set to those genes that show the greatest differences across your class variable. Also if you have relatively little experience with R I would suggest using a linear modeling package such as Limma since it has excellent documentation and many examples that are easy to follow.
I'm working on a project now that's rather unlike anything I've done before. I have two tests with binary results that will be administered to the same sample, which is drawn from a clustered population (i.e., some subjects will be from the same family). I'd like to compare proportions of positive test results, but the clustering makes McNemar's test inappropriate so I've been reading up on alternative approaches. The two main routes seem to be 1) the clustering-adjusted McNemar alternatives by Rao and Scott (1992), Eliasziw and Donner (1991), and Obuchowski (1998), and 2) GEE.
Do you know of any implementations of the Rao-Obuchowski lineage in R (or, I suppose, SAS)? GEE is easy to find, but have you had a positive or negative experience with any particular packages? Is there another route to analyzing these data that I'm completely missing?
You could always just use a clustered bootstrap. Resample across families, which you believe are independent. That is, keep families together when you resample. Compute p2 - p1 for each sample. After 1000 iterations or so, compute the upper and bottom 2.5% quantiles. This will give you a bootstrapped 95% confidence interval. Alternatively compute the fraction of samples above zero, or whatever your hypothesis is. The procedure should have good pretty good properties unless the number of families is small.
It's probably easiest to do this by hand in R rather than relying on any package.
Check out the survey package: it is designed to take into account correlations induced by clustered sampling.
Have you already checked the CorrBin package in R?
It is for analysis of correlated binary data, there is a paper named: Using the CorrBin package for nonparametric analysis of
correlated binary data by Szabo, it includes the Rao-Scott, stochastic ordering and three versions of a GEE-based test.
The clust.bin.pair package for clustered binary matched-pair data was recently published to CRAN.
It contains implementations of Eliasziw and Donner (1991) and Obuchowski (1998), as well as two more recent tests in the same family Durkalski (2003) and Yang (2010).