28
votes
0answers
1k views

Variance on the sum of predicted values from a mixed effect model on a timeseries

I have a mixed effect model (in fact a generalized additive mixed model) that gives me predictions for a timeseries. To counter the autocorrelation, I use a corCAR1 model, given the fact I have ...
16
votes
0answers
524 views

SVD of correlated matrix should be additive but doesn't appear to be

I'm just trying to replicate a claim made in the following paper, Finding Correlated Biclusters from Gene Expression Data, which is: Proposition 4. If $X_{IJ}=R_{I}C^{T}_{J}$. then we have: ...
10
votes
0answers
123 views

Training a basic Markov Random Field for classifying pixels in an image

I am attempting to learn how to use Markov Random Fields to segment regions in an image. I do not understand some of the parameters in the MRF or why the expectation maximisation I perform fails to ...
10
votes
0answers
215 views

Can the Mantel test be extended to asymmetric matrices?

The Mantel test is usually applied to symmetric distance/difference matrices. As far as I understand, an assumption of the test is that the measure used to define differences must be at least a ...
10
votes
0answers
213 views

Phylogenetic dependent variables: ANOVA?

I understand deriving a covariance matrix from phylogenetic data to make $cov(X,Y) = 0$ for two variables you're making a regression on. But what happens if you have one continuous variable, that ...
9
votes
0answers
1k views

How do you select variables in a regression model?

The traditional approach to variable selection is to find variables that contribute the most to predicting a new response. Recently I learned of an alternative to this. In modeling variables that ...
8
votes
0answers
139 views

Is there a Bayesian approach to density estimation

I am interested to estimate the density of a continuous random variable $X$. One way of doing this that I learnt is the use of Kernel Density Estimation. But now I am interested in a Bayesian ...
8
votes
0answers
1k views

Inverting the Fourier Transform for a Fisher distribution

The characteristic function of the Fisher$(1,\alpha)$ distribution is: $$C(t)=\frac{\Gamma \left(\frac{\alpha +1}{2}\right) U\left(\frac{1}{2},1-\frac{\alpha }{2},-i t \alpha \right)}{\Gamma ...
8
votes
0answers
148 views

Paper on performing hypothesis tests based on outcome of another test

It is well known that it is problematic to choose a statistical test based on the outcome of another statistical test, as the p-values are difficult to impossible to interpret (e.g. Choosing a ...
8
votes
0answers
175 views

Inference on fixed effects in a mixed effects model

I have correlated data and am using a logistic regression mixed effects model to estimate the individual level (conditional) effect for a predictor of interest. I know that for standard marginal ...
8
votes
0answers
879 views

Are categorical variables standardized differently in penalized regression?

In penalized/regularized regression (lasso, ridge, etc.) the predictors are typically standardized to be centered at 0 and often to have variance 1. Are categorical predictors treated differently. If ...
8
votes
0answers
145 views

Penalized spline confidence intervals based on cluster-sandwich VCV

This is my first post here, but I've benefited a lot from this forum's results popping up in google search results. I've been teaching myself semi-parametric regression using penalized splines. ...
8
votes
0answers
306 views

Gaussian Like distribution with higher order moments

For the Gaussian distribution with unknown mean and variance, the sufficient statistics in the standard exponential family form is $T(x)=(x,x^2)$. I have a distribution that has ...
8
votes
0answers
278 views

Updating classification probability in logistic regression through time

I am building a predictive model that forecasts a student's probability of success at the end of a term. I’m specifically interested in whether the student succeeds or fails, where success is usually ...
8
votes
0answers
707 views

Intraclass Correlation Coefficients (ICC) with Multiple Variables

Suppose I have measured some variable in siblings, which are nested within families. The data structure looks like this: family sibling value ------ ------- ----- 1 1 y_11 1 2 ...
8
votes
0answers
940 views

How to analyse repeated measure ANOVA with three or more conditions presented in randomised order?

Context: My question concerns a typical design in my area – a researcher takes a group of subjects (say 10) and then applies three different conditions to them to measure the change in a response ...
7
votes
0answers
109 views

Given loads of data, can we always model it with polynomials?

Given Taylor series and enough data so as to not risk over-fitting, do you actually need to think about if your phenomenon is following an exponential, quadratic, logarithmic, ..., behaviour? I'm sure ...
7
votes
0answers
169 views

Model selection with Firth logistic regression

In a small data set ($n\sim100$ ) that I am working with, several variables give me perfect prediction/separation. I thus use Firth logistic regression to deal with the issue. If I select the best ...
7
votes
0answers
147 views

Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
7
votes
0answers
157 views

Issues with ordinary kriging

I was following this wiki article related to ordinary kriging Now my covariance matrix looks like this, for 4 variables ...
7
votes
0answers
173 views

p-value adjustment for Local Moran's I statistic (LISA)

I'm working with some exploratory spatial analysis in R using spdep package. I came across an option to adjust p-values of local indicators of spatial association (LISA) calculated using ...
7
votes
0answers
217 views

Unique (?) idea for forecasting sales

I'm working on developing a model to predict total sales of a product. I have about a year and a half of bookings data, so I could do a standard time series analysis. However, I also have a lot of ...
7
votes
0answers
103 views

Testing certain contrasts: Is this provably a hard problem, or not?

I posted this to mathoverflow and no one's answering: Scheffé's method for identifying statistically significant contrasts is widely known. A contrast among the means $\mu_i$, $i=1,\ldots,r$ of $r$ ...
7
votes
0answers
105 views

Analyze a football match: similar players with DBSCAN and similar trajectories with TRACLUS

I'm trying to analyze a dataset that originates from sensors located near players' shoes in a match (http://www.orgs.ttu.edu/debs2013/index.php?goto=cfchallengedetails). I decided to look at ...
7
votes
0answers
323 views

Clustered standard errors vs. multilevel modeling?

I've skimmed through several books (Raudenbush & Bryk, Snijders & Bosker, Gelman & Hill, etc.) and several articles (Gelman, Jusko, Primo & Jacobsmeier, etc.), and I still haven't ...
7
votes
0answers
240 views

Luce choice axiom, question about conditional probability

I'm reading Luce (1959). Then I found this statement: When a person chooses among alternatives, very often their responses appear to be governed by probabilities that are conditioned on the ...
7
votes
0answers
166 views

AIC/BIC: how many parameters does a permutation count for?

Let's say I have a model selection problem and I am trying to use AIC or BIC to evaluate the models. This is straightforward for models that have some number $k$ of real-valued parameters. However, ...
7
votes
0answers
209 views

Rao-Blackwellization of sequential Monte Carlo filters

In the seminal paper "Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks" by A. Doucet et. al. a sequential monte carlo filter (particle filter) is proposed, which makes use of a ...
7
votes
0answers
177 views

Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions ...
7
votes
0answers
325 views

Calculating prediction intervals when using cross validation

Are standard deviation estimates calculated via: $ s_N = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}. $ (http://en.wikipedia.org/wiki/Standard_deviation#Sample_standard_deviation) for ...
7
votes
0answers
209 views

$ARIMA(p,d,q)+X_t$, Simulation over Forecasting period

I have time series data and I used an $ARIMA(p,d,q)+X_t$ as the model to fit the data. The $X_t$ is an indicator random variable that is either 0 (when I don’t see a rare event) or 1 (when I see the ...
7
votes
0answers
294 views

What are the options in proportional hazard regression model when Schoenfeld residuals are not good?

I am doing a Cox proportional hazards regression in R using coxph, which includes many variables. The Martingale residuals look great, and the Schoenfeld residuals ...
7
votes
0answers
829 views

Multiple imputation questions for multiple regression in SPSS

I am currently running a multiple regression model using imputed data and have a few questions. Background: Using SPSS 18. My data appears to be MAR. Listwise deletion of cases leaves me with only ...
7
votes
0answers
950 views

Random forests for multivariate regression

I have a multi-output regression problem with $d_x$ input features and $d_y$ outputs. The outputs have a complex, non-linear correlation structure. I'd like to use random forests to do the ...
7
votes
0answers
1k views

How to analyze longitudinal count data: accounting for temporal autocorrelation in GLMM?

Hello statistical gurus and R programming wizards, I am interested in modeling animal captures as a function of environmental conditions and day of the year. As part of another study, I have counts ...
7
votes
0answers
414 views

What data and statistics skills are currently in high demand and where are they in high demand?

I have a job doing data analysis in finance. My current job is such that I don't have much exposure to things happening in the rest of my industry or other industries. I have a fair amount of ...
7
votes
0answers
880 views

How to use G Power 3 to calculate statistical power in mixed design ANOVA with unequal group sample sizes

In G power 3, ANOVA repeated measures within-between interaction: Only the total sample size is reported assuming equal sample size for the two groups. My questions are: How would it work if the ...
7
votes
0answers
486 views

How can I assess GEE/logistic model fit when covariates have some missing data?

I have fit two generalized estimating equation (GEE) models to my data: 1) Model 1: Outcome is longitudinal Yes/No variable (A) (year 1,2,3,4,5) with longitudinal continuous predictor (B) for years ...
6
votes
0answers
187 views

Multivariant time series in R. How to find lagged correlation and build model for forecasting

I'm new in the page and pretty new in statistics and R. I'm working on a project for college with the objective of finding the correlation between rain and water flow level in rivers. Once the ...
6
votes
0answers
241 views

What does $(X'X)^{-1}$ mean?

In a regression what is the matrix $(X'X)^{-1}$? what do its interior elements represent? Can anyone tell me which values in a stata regression are represented by $(X'X)^{-1}$?
6
votes
0answers
155 views

If the distribution is bimodal, does p-value mean anything?

P-value is defined the probability of obtaining a test-statistic at least as extreme as what is observed, assuming null-hypothesis is true. In other words, $$P( X \ge t | H_0 )$$ But what if the ...
6
votes
0answers
92 views

Why not use Beta(1,1) as boundary avoiding prior on a transformed correlation parameter?

In Bayesian Data Analysis, chapter 13, page 317, second full paragraph, in the modal and distributional approximations, Gelman et al. write: If the plan is to summarize inference by the posterior ...
6
votes
0answers
237 views

What is the difference between conditional and unconditional quantile regression?

The conditional quantile regression estimator by Koenker and Basset (1978) for the $\tau^{th}$ quantile is defined as $$\widehat{\beta}_{QR} = \min_{b} \sum^{n}_{i=1} \rho_\tau (y_i - X'_i b_\tau)$$ ...
6
votes
0answers
224 views

Instrumental variables and mixed/multilevel models

I want to estimate a growth model to model the growth trajectories of individuals $j$ over multiple time points $t$ by applying a standard mixed/mutilevel model (also known as random coefficient ...
6
votes
0answers
101 views

Why is using cross-sectional data to infer / predict longitudinal changes a Bad Thing?

I'm looking for a paper which I hope exists, but don't know if it does. It could be a set of case studies, and / or an argument from probability theory, about why using cross-sectional data to infer / ...
6
votes
0answers
1k views

What does the anova() command do with a lmer model object?

Hopefully this is a question that someone here can answer for me on the nature of decomposing sums of squares from a mixed-effects model fit with lmer (from the ...
6
votes
0answers
115 views

Detecting outliers using 95% PI around a natural spline fit

Please see the picture below: I wanted to mark the points that are not consistent with their adjacent points as outlier. What I did was to fit a natural spline fit to 1000 observations (the purple ...
6
votes
0answers
175 views

Interpretation of Bayesian 95% prediction interval

Assume the following bivariate regression model: $$ y_i = \beta x_i + u_i, $$ where $u_i$ is i.i.d $N(0, \sigma^2 = 9)$ for $i = 1,\ldots, n$. Assume a noninformative prior $p(\beta) \propto ...
6
votes
0answers
459 views

Anomaly Detection with Dummy Features (and other Discrete/Categorical Features)

Intro This is my first time posting on here, so please, if anything doesn't seem technically correct, either in the formatting, or the use of correct definitions, I'm interested to know what ...
6
votes
0answers
292 views

Cholesky versus eigendecomposition for drawing samples from a multivariate normal distribution

I would like to draw a sample $\mathbf{x} \sim N\left(\mathbf{0}, \mathbf{\Sigma} \right)$. Wikipedia suggests either using a Cholesky or Eigendecomposition, i.e. $ \mathbf{\Sigma} = ...

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