Jake Westfall
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Maximum Likelihood Estimation (MLE) in layman terms
39 votes

The maximum likelihood (ML) estimate of a parameter is the value of that parameter under which your actual observed data are most likely, relative to any other possible values of the parameter. The ...

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What are the worst (commonly adopted) ideas/principles in statistics?
38 votes

Post hoc power analysis That is, using power analysis after a study has been completed rather than before, and in particular plugging in the observed effect size estimate, sample size, etc. Some ...

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Confused about independent probabilities. If a fair coin is flipped 5 times, P(HHHHH) = 0.03125, but P(H | HHHH) = 0.5
37 votes

P(HHHHH) There are 32 possible outcomes from flipping a coin 5 times. Here they are listed: HHHHH THHHH HTHHH TTHHH HHTHH THTHH HTTHH TTTHH HHHTH THHTH HTHTH TTHTH HHTTH THTTH HTTTH TTTTH HHHHT THHHT ...

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Big disagreement in the slope estimate when groups are treated as random vs. fixed in a mixed model
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35 votes

There are several things going on here. These are interesting issues, but it will take a fair amount of time/space to explain it all. First of all, this all becomes a lot easier to understand if we ...

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Why is the marginal distribution/marginal probability described as "marginal"?
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29 votes

Consider the table below (copied from this website) representing joint probabilities of outcomes from rolling two dice: In this common and natural way of showing the distribution, the marginal ...

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Showing that 100 measurements for 5 subjects provide much less information than 5 measurements for 100 subjects
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26 votes

The short answer is that your conjecture is true when and only when there is a positive intra-class correlation in the data. Empirically speaking, most clustered datasets most of the time show a ...

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Why does treatment coding result in a correlation between random slope and intercept?
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25 votes

Treatment coding doesn't always or necessarily result in intercept/slope correlation, but it tends to more often than not. It's easiest to see why this is the case using pictures, and considering the ...

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What is the upside of treating a factor as random in a mixed model?
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21 votes

1. A famous example in psychology and linguistics is described by Herb Clark (1973; following Coleman, 1964): "The language-as-fixed-effect fallacy: A critique of language statistics in psychological ...

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Why does statsmodels.api.OLS over-report the r-squared value?
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20 votes

This is not technically an error in statsmodels, rather it is because statsmodels.OLS does not add the intercept/constant term to the right-hand-side of the regression equation by default -- you have ...

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Suppression effect in regression: definition and visual explanation/depiction
20 votes

Here is another geometric view of suppression, but rather than being in the observation space as @ttnphns's example is, this one is in the variable space, the space where everyday scatterplots live. ...

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What is the lme4::lmer equivalent of a three-way repeated measures ANOVA?
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19 votes

The direct answer to your question is that the last model you wrote, anova(lmer(y ~ a*b*c +(1|subject) + (1|a:subject) + (1|b:subject) + (1|c:subject) + (1|a:b:subject) + (1|a:c:subject) +...

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Regression: why test normality of overall residuals, instead of residuals conditional on $\hat{y}$?
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18 votes

Couldn't we have normal residuals at each predicted value of y, while having overall residuals that were quite non-normal? No -- at least, not under the standard assumption that the variance of the ...

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Why do I get zero variance of a random effect in my mixed model, despite some variation in the data?
18 votes

I don't think there's a problem. The lesson from the model output is that although there is "obviously" variation in subject performance, the extent of this subject variation can be fully or virtually-...

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In math/stats terminology, $1/p$ is the reciprocal of $p$. So what is $1-p$ called, if anything?
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18 votes

Assuming $p$ is the probability of an event, $1 - p$ is the probability of its complement. If $p$ is not the probability of an event then I doubt that $1 - p$ has any special meaning or name.

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Is R's glm function useless in a big data / machine learning setting?
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16 votes

The unregularized model is suffering from complete separation because you are trying to predict the dichotomized variable price_c from the continuous variable price from which it is derived. The ...

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Equivalence between a repeated measures anova model and a mixed model: lmer vs lme, and compound symmetry
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15 votes

As Ben Bolker already mentioned in the comments, the problem is as you suspect: The lmer() model gets tripped up because it attempts to estimate a variance component model, with the variance component ...

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Does $r$-squared have a $p$-value?
15 votes

In addition to the numerous (correct) comments by other users pointing out that the $p$-value for $r^2$ is identical to the $p$-value for the global $F$ test, note that you can also get the $p$-value ...

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How to partition the variance explained at group level and at individual level?
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15 votes

Yes, there is a consensus: you should use the variances, not the standard deviations, in computing the intra-class correlation (ICC). The two-level random-intercept-only model is $$ y_{ij} = \beta_0 +...

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What does pooled variance "actually" mean?
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14 votes

Put simply, the pooled variance is an (unbiased) estimate of the variance within each sample, under the assumption/constraint that those variances are equal. This is explained, motivated, and ...

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Intraclass Correlation Coefficient in mixed model with random slopes
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13 votes

Basically there's no single number or estimate that can summarize the degree of clustering in a random slopes model. The intra-class correlation (ICC) can only be written as a simple proportion of ...

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Mixed effects model: Compare random variance component across levels of a grouping variable
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12 votes

There's more than one way to test this hypothesis. For example, the procedure outlined by @amoeba should work. But it seems to me that the simplest, most expedient way to test it is using a good old ...

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Relationships between correlation and causation
12 votes

The fourth point is an example of Berkson's paradox, also known as conditioning on a collider, also known as the explaining-away phenomenon. As an example, consider a young woman who is frequently ...

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Adding random effect influences coefficient estimates
12 votes

"I have always been taught that random effects only influence the variance (error), and that fixed effects only influence the mean." As you have discovered, this is only true for balanced, complete (...

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Can I probe cross-level interactions without random slope in a hierarchical linear model?
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12 votes

Having random slopes at level 1 is not a necessary condition for examining cross-level interactions. All that is necessary is that you have 2 predictors that vary at different levels, and their ...

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Unpaired repeated measures data
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11 votes

A simple two-sample t-test would actually be a conservative way of testing for time differences here. Let's say that $t_{paired}$ is the t-statistic that you would get from a paired t-test on your ...

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Is there a rule of thumb for using standard deviation of k-fold cross-validation scores to pick the best model?
Accepted answer
11 votes

Sort of. There is the so-called "one standard error rule," which does use the standard deviation of the prediction error estimates, although not in quite the way you mentioned: instead you divide the ...

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z-score and Normal Distribution
11 votes

Technically, z-scoring does not depend on any distributional assumptions, such as normality. It's just a way of describing how far observations are from the mean, no matter what the distribution ...

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Design of matrix of contrasts in R
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11 votes

Your last 2 contrasts are right, but the first 3 are wrong. We can verify this by figuring out the linear combinations of coefficients that give each group mean, and then constructing the desired ...

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Regressing out a variable?
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10 votes

Although it is not the most commonly used phrase (in my experience), as used in the question you linked to, to "regress out" a third variable is synonymous with "partialling out," "controlling for," "...

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How is the Spearman-Brown prophecy formula affected by questions of differing difficulties?
10 votes

Although I feel a little sheepish contradicting both a "respected text" as well as another CV user, it seems to me that the Spearman-Brown formula is not affected by having items of differing ...

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