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1500 questions
69
votes
5 answers

What is the difference between a "nested" and a "non-nested" model?

In the literature on hierarchical/multilevel models I have often read about "nested models" and "non-nested models", but what does this mean? Could anyone maybe give me some examples or tell me about the mathematical implications of this phrasing?
llama
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69
votes
6 answers

Real-life examples of moving average processes

Can you give some real-life examples of time series for which a moving average process of order $q$, i.e. $$ y_t = \sum_{i=1}^q \theta_i \varepsilon_{t-i} + \varepsilon_t, \text{ where } \varepsilon_t \sim \mathcal{N}(0, \sigma^2) $$ has some a…
weez13
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69
votes
9 answers

Taleb and the Black Swan

Taleb's book "The Black Swan" was a New York Times best seller when it came out several years ago. The book is now in its second edition. After meeting with statisticians at a JSM (an annual statistical conference), Taleb toned down his criticism…
Michael R. Chernick
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69
votes
9 answers

Advanced statistics books recommendation

There are several threads on this site for book recommendations on introductory statistics and machine learning but I am looking for a text on advanced statistics including, in order of priority: maximum likelihood, generalized linear models,…
Robert Kubrick
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69
votes
3 answers

Questions about how random effects are specified in lmer

I recently measured how the meaning of a new word is acquired over repeated exposures (practice: day 1 to day 10) by measuring ERPs (EEGs) when the word was viewed in different contexts. I also controlled properties of the context, for instance, its…
alwin hoff
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69
votes
4 answers

Does it make sense to add a quadratic term but not the linear term to a model?

I have a (mixed) model in which one of my predictors should a priori only be quadratically related to the predictor (due to the experimental manipulation). Hence, I would like to add only the quadratic term to the model. Two things keep me from…
Henrik
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69
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4 answers

Are there cases where PCA is more suitable than t-SNE?

I want to see how 7 measures of text correction behaviour (time spent correcting the text, number of keystrokes, etc.) relate to each other. The measures are correlated. I ran a PCA to see how the measures projected onto PC1 and PC2, which avoided…
user3744206
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69
votes
5 answers

How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?

I used to think that "random effects model" in econometrics corresponds to a "mixed model with random intercept" outside of econometrics, but now I am not sure. Does it? Econometrics uses terms like "fixed effects" and "random effects" somewhat…
amoeba
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69
votes
8 answers

What is a good, convincing example in which p-values are useful?

My question in the title is self explanatory, but I would like to give it some context. The ASA released a statement earlier this week “on p-values: context, process, and purpose”, outlining various common misconceptions of the p-value, and urging…
Tal Galili
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69
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3 answers

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?
Andrew
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69
votes
3 answers

References containing arguments against null hypothesis significance testing?

In the last few years I've read a number of papers arguing against the use of null hypothesis significance testing in science, but didn't think to keep a persistent list. A colleague recently asked me for such a list, so I thought I'd ask everyone…
Mike Lawrence
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69
votes
6 answers

Find expected value using CDF

I'm going to start out by saying this is a homework problem straight out of the book. I have spent a couple hours looking up how to find expected values, and have determined I understand nothing. Let $X$ have the CDF $F(x) = 1 - x^{-\alpha},…
styfle
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68
votes
3 answers

What is the effect of having correlated predictors in a multiple regression model?

I learned in my linear models class that if two predictors are correlated and both are included in a model, one will be insignificant. For example, assume the size of a house and the number of bedrooms are correlated. When predicting the cost of a…
Vivek Subramanian
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68
votes
5 answers

What is a contrast matrix?

What exactly is contrast matrix (a term, pertaining to an analysis with categorical predictors) and how exactly is contrast matrix specified? I.e. what are columns, what are rows, what are the constraints on that matrix and what does number in…
Tomas
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68
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5 answers

Is a sample covariance matrix always symmetric and positive definite?

When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix? Currently my problem has a sample of 4600 observation vectors and 24 dimensions.
Morten
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