# Tagged Questions

A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but ...

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### Including the interaction but not the main effects in a model

Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
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### Is there any reason to prefer the AIC or BIC over the other?

The AIC and BIC are both methods of assessing model fit penalized for the number of estimated parameters. As I understand it, BIC penalizes models more for free parameters than does AIC. Beyond a ...
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### Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?

In what circumstances would you want to, or not want to scale or standardize a variable prior to model fitting? And what are the advantages / disadvantages of scaling a variable?
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### Do all interactions terms need their individual terms in regression model?

I am actually reviewing a manuscript where the authors compare 5-6 logit regression models with AIC. However, some of the models have interaction terms without including the individual covariate ...
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### Weakly informative prior distributions for scale parameters

I have been using log normal distributions as prior distributions for scale parameters (for normal distributions, t distributions etc.) when I have a rough idea about what the scale should be, but ...
640 views

### Practical thoughts on explanatory vs predictive modeling [duplicate]

Possible Duplicate: Practical thoughts on explanatory vs. predictive modeling This question has been bugging me for some time, and I was going to write a blog post about it. However, I ...
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### How to fit an ARIMAX-model with R?

I have four different time series of hourly measurements: The heat consumption inside a house The temperature outside the house The solar radiation The wind speed I want to be able to predict the ...
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### Why does including latitude and longitude in a GAM account for spatial autocorrelation?

I have produced generalized additive models for deforestation. To account for spatial-autocorrelation, I have included latitude and longitude as a smoothed, interaction term (i.e. s(x,y)). I've based ...
239 views

### Problem with calculating $R^2$

I believe I have rather simple question but I would like to make it right. I have already asked question, however I am not sure whether I did everything correct or there is a mistake in the answer ...
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### Why is variable selection necessary?

Common data-based variable selection procedures (for example, forward, backward, stepwise, all subsets) tend to yield models with undesirable properties, including: Coefficients biased away from ...
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### Forecasting time series based on a behavior of other one

Apologies for this vague and unclear question, I have no background in statistics. I have two vectors of time series data, covering a six month period. The data is in daily intervals (except for ...
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### Either quadratic or interaction term is significant in isolation, but neither are together

As part of an assignment, I had to fit a model with two predictor variables. I then had to draw a plot of the models' residuals against one of the included predictors and make changes based on that. ...
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### What is the benefit of breaking up a continuous predictor variable?

I'm wondering what the value is in taking a continuous predictor variable and breaking it up (e.g., into quintiles), before using it in a model. It seems to me that by binning the variable we lose ...
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### Is interaction possible between two continuous variables?

All of my variables are continuous. There are no levels. Is it possible to even have interaction between the variables?
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### Model evaluation and comparison for selecting the best model

When comparing results obtained with different models in R, what should I look for to select the best one? If I use for example the following 4 models applied to the same presence/absence sample ...
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### Can someone explain Gibbs sampling in very simple words?

I'm doing some reading on topic modeling (with Latent Dirichlet Allocation) which makes use of Gibbs sampling. As a newbie in statistics -- well, I know things like binomials, multinomials, priors etc ...
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### What is a “saturated” model?

What is meant when we say we have a saturated model?
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### Understanding the parameters inside the Negative Binomial Distribution

I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of ...
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### Model for population density estimation

A database of (population, area, shape) can be used to map population density by assigning a constant value of population/area to each shape (which is a polygon such as a Census block, tract, county, ...
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### When will a less true model predict better than a truer model?

In "To Explain or to Predict?", Pr. Galit Shmueli said that sometimes a less true model can predict better than a truer model. Why is it so? When will it happen? How does it happen? Is explanation a ...
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### What is the community's take on the Fourth Quadrant?

Nassim Taleb, of Black Swan fame (or infamy), has elaborated on the concept and developed what he calls "a map of the limits of Statistics". His basic argument is that there is one kind of decision ...
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### Properties of logistic regressions

We're working with some logistic regressions and we have realized that the average estimated probability always equals the proportion of ones in the sample; that is, the average of fitted values ...
347 views

### Concepts behind fixed/random effects models

Can someone help me to understand fixed/random effect models? You may either explain in your own way if you have digested these concepts or direct me to the resource (book, notes, website) with ...
651 views

### Looking for good introductory treatment of meta-analysis

A (non-statistician) colleague has been encountering meta-analyses in papers he reviews for medical journals and is looking for a good introductory level treatment so he can educate himself. Any ...
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### Identify probability distributions

Given a sample data set of floating point numbers, how do we determine its probability distribution and prove it? Also generate random numbers of the same distributions thereafter.
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### Is it problematic if one predictor in a set accounts for almost all the prediction?

I am running a logistic regression with customer event data with multiple predictors. However, one variable is extremely important, alone predicting 60% of the customers for the event. When this main ...
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### Generating likely populations given a subsample and control totals

Context In transportation planning, agent-based microsimulation is a method to deal with the complexity of the problem. Instead of computing aggregate flows (as in the classical four-step model), ...
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### Which model should I use to fit my data ? ordinal and non-ordinal, not normal and not homoscedastic

Here is the kind of data I have: I have two predictor variables: 1) discrete non-ordinal --> c('a','b','c') 2) discrete ordinal --> c(10,100,200,500) Response variable: Proportion of TRUE over a ...
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### Rules of thumb for “modern” statistics

I like G van Belle's book on Statistical Rules of Thumb, and to a lesser extent Common Errors in Statistics (and How to Avoid Them) from Phillip I Good and James W. Hardin. They address common ...
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### Statistical models cheat sheet

I was wondering if you know if a stastical model "cheat sheet(s)" that lists any or more information: When to use the model When not to use the model required and optional inputs expected outputs ...
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### Model for predicting number of Youtube views of Gangnam Style

PSY's music video "Gangnam style" is popular, after a little more than 2 months it has about 540 million viewers. I learned this from my preteen children at dinner last week and soon the discussion ...
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### When to use multiple models for prediction?

This is a fairly general question: I have typically found that using multiple different models outperforms one model when trying to predict a time series out of sample. Are there any good papers ...
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### General Linear Model vs. Generalized Linear Model (with an identity link function?)

This is my first post, so please take it easy on me if I am not following some standards! I did a search for my question and nothing came up. My question relates mostly around the practical ...
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### What are best practices in identifying interaction effects?

Other than literally testing each possible combination of variable(s) in a model (x1:x2 or x1*x2 ... xn-1 * xn). How do you ...
2k views

### What is so cool about de Finetti's representation theorem?

From Theory of Statistics by Mark J. Schervish (page 12): Although DeFinetti's representation theorem 1.49 is central to motivating parametric models, it is not actually used in their ...
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### Tools for modeling financial time series

What modern tools (Windows-based) do you suggest for modeling financial time series?
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### What is the meaning of “All models are wrong, but some are useful”

"Essentially, all models are wrong, but some are useful." --- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339. What ...
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### How to combine confidence intervals for a variance component of a mixed-effects model when using multiple imputation

The logic of multiple imputation (MI) is to impute the missing values not once but several (typically M=5) times, resulting in M completed datasets. The M completed datasets are then analyzed with ...
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### Spatial statistics models — CAR vs SAR

When would one prefer to use a Conditional Autoregressive model over a Simultaneous Autoregressive model when modelling autocorrelated geo-referenced areal data?
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### Poisson regression with large data: is it wrong to change the unit of measurement?

Due to the factorial in a poisson distribution, it becomes unpractical to estimate poisson models (for example, using maximum likelihood) when the observations are large. So, for example, if I am ...
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### What is the relationship between R-squared and p-value in a regression?

tl;dr - for OLS regression, does a higher R-squared also imply a higher P-value? Specifically for a single explanatory variable (Y = a + bX + e) but would also be interested to know for n multiple ...
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### What are some standard practices for creating synthetic data sets?

As context: When working with a very large data set, I am sometimes asked if we can create a synthetic data set where we "know" the relationship between predictors and the response variable, or ...
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### Communicating Regression Model Results

I am concerned about how unequipped most people are (both within and without academia) to properly employ standard model building methods such as linear regression and to interpret the results of ...
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### Is a logistic regression biased when the outcome variable is split 5% - 95%?

I am building a propensity model using logistic regression for a utility client. My concern is that out of the total sample my 'bad' accounts are just 5%, and the rest are all good. I am predicting ...
289 views

### Are these equivalent representations of the same hierarchical Bayesian model?

If $X$ is a categorical variable, and I am interested in the posterior distributions of $\beta_1$, where $\beta_1$ is a vector of coefficients, one for each level of X, are these equivalent models? ...
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### Variables importance: who can do the most pushups?

I don't know enough math to formulate an intelligent question on this so I'll give an example. I'd like an answer to my example but also I'd like to know the jargon I need to be able to research it ...
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### Finding the distribution and/or fitting a model (to a biological problem)

I am a bioinformatician and work on RNA-Seq data. The data contains a lot of reads (of length 80 bp in my case). These reads are fragments of those genes that were expressed. I map them back to my ...
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### Models for Generalized Estimating Equation?

From Wikipedia, Generalized Estimating Equation (GEE) is a method to estimate the parameters of a generalized linear model (with an exponential family distribution for the response). By reading other ...
I have a set of $n=1000$ samples of 4 dimensions (multivariate) where each measurement obtained from GPS tracking data is taken at a time interval representing spatial coordinates $(x,y)$, velocity. ...