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189
votes
8answers
82k views

Algorithms for automatic model selection

I would like to implement an algorithm for automatic model selection. I am thinking of doing stepwise regression but anything will do (it has to be based on linear regressions though). My problem ...
294
votes
16answers
97k views

Is normality testing 'essentially useless'?

A former colleague once argued to me as follows: We usually apply normality tests to the results of processes that, under the null, generate random variables that are only asymptotically or ...
127
votes
5answers
56k views

What should I do when my neural network doesn't learn?

I'm training a neural network but the training loss doesn't decrease. How can I fix this? I'm not asking about overfitting or regularization. I'm asking about how to solve the problem where my ...
141
votes
6answers
74k views

Can a probability distribution value exceeding 1 be OK?

On the Wikipedia page about naive Bayes classifiers, there is this line: $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve ...
238
votes
16answers
456k views

What is the meaning of p values and t values in statistical tests?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
941
votes
28answers
549k views

Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
97
votes
7answers
31k views

Why is accuracy not the best measure for assessing classification models?

This is a general question that was asked indirectly multiple times in here, but it lacks a single authoritative answer. It would be great to have a detailed answer to this for the reference. ...
295
votes
10answers
283k views

Difference between logit and probit models

What is the difference between Logit and Probit model? I'm more interested here in knowing when to use logistic regression, and when to use Probit. If there is any literature which defines it using ...
160
votes
8answers
147k views

How to deal with perfect separation in logistic regression?

If you have a variable which perfectly separates zeroes and ones in target variable, R will yield the following "perfect or quasi perfect separation" warning message: ...
254
votes
11answers
150k views

How to understand degrees of freedom?

From Wikipedia, there are three interpretations of the degrees of freedom of a statistic: In statistics, the number of degrees of freedom is the number of values in the final calculation of a ...
114
votes
9answers
102k views

When is it ok to remove the intercept in a linear regression model?

I am running linear regression models and wondering what the conditions are for removing the intercept term. In comparing results from two different regressions where one has the intercept and the ...
270
votes
7answers
245k views

When conducting multiple regression, when should you center your predictor variables & when should you standardize them?

In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized. (Standardizing consists in subtracting the mean and dividing ...
109
votes
3answers
31k views

What if residuals are normally distributed, but y is not?

I've got a weird question. Assume that you have a small sample where the dependent variable that you're going to analyze with a simple linear model is highly left skewed. Thus you assume that $u$ is ...
230
votes
6answers
29k views

Is $R^2$ useful or dangerous?

I was skimming through some lecture notes by Cosma Shalizi (in particular, section 2.1.1 of the second lecture), and was reminded that you can get very low $R^2$ even when you have a completely linear ...
68
votes
8answers
10k views

What is meant by a “random variable”?

What do they mean when they say "random variable"?
79
votes
3answers
68k views

Does an unbalanced sample matter when doing logistic regression?

Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables. My problem is the following: ...
164
votes
2answers
233k views

When (and why) should you take the log of a distribution (of numbers)?

Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company... Now someone (or some formula) comes along and says "let's take/use ...
57
votes
6answers
12k views

Principled way of collapsing categorical variables with many levels?

What techniques are available for collapsing (or pooling) many categories to a few, for the purpose of using them as an input (predictor) in a statistical model? Consider a variable like college ...
160
votes
8answers
310k views

In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?

Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
223
votes
12answers
65k views

Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
90
votes
11answers
54k views

Maximum Likelihood Estimation (MLE) in layman terms

Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation.
49
votes
2answers
14k views

Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?

The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other ...
105
votes
6answers
12k views

Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?

For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
76
votes
7answers
27k views

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 ...
338
votes
3answers
208k views

Relationship between SVD and PCA. How to use SVD to perform PCA?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
52
votes
5answers
53k views

Best practice when analysing pre-post treatment-control designs

Imagine the following common design: 100 participants are randomly allocated to either a treatment or a control group the dependent variable is numeric and measured pre- and post- treatment Three ...
108
votes
4answers
29k views

Assessing approximate distribution of data based on a histogram

Suppose I want to see whether my data is exponential based on a histogram (i.e. skewed to the right). Depending on how I group or bin the data, I can get wildly different histograms. One set of ...
399
votes
21answers
195k views

Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
143
votes
7answers
112k views

PCA on correlation or covariance?

What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?
199
votes
3answers
18k views

How to know that your machine learning problem is hopeless?

Imagine a standard machine-learning scenario: You are confronted with a large multivariate dataset and you have a pretty blurry understanding of it. What you need to do is to make predictions ...
43
votes
3answers
46k views

Interpretation of log transformed predictor and/or response

I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed. Consider the case of <...
90
votes
3answers
26k views

Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?

Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance ...
136
votes
5answers
189k views

How exactly does one “control for other variables”?

Here is the article that motivated this question: Does impatience make us fat? I liked this article, and it nicely demonstrates the concept of “controlling for other variables” (IQ, career, income, ...
71
votes
10answers
34k views

What is a complete list of the usual assumptions for linear regression?

What are the usual assumptions for linear regression? Do they include: a linear relationship between the independent and dependent variable independent errors normal distribution of errors ...
84
votes
17answers
67k views

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?
81
votes
0answers
64k views

How can a regression be significant yet all predictors be non-significant? [duplicate]

My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity ...
91
votes
7answers
75k views

How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
41
votes
4answers
13k views

Why do statisticians say a non-significant result means “you can't reject the null” as opposed to accepting the null hypothesis?

Traditional statistical tests, like the two sample t-test, focus on trying to eliminate the hypothesis that there is no difference between a function of two independent samples. Then, we choose a ...
46
votes
5answers
9k views

When is unbalanced data really a problem in Machine Learning?

We already had multiple questions about unbalanced data when using logistic regression, SVM, decision trees, bagging and a number of other similar questions, what makes it a very popular topic! ...
259
votes
9answers
472k views

What is the difference between fixed effect, random effect and mixed effect models?

In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect and mixed effect models?
42
votes
1answer
33k views

How to interpret type I, type II, and type III ANOVA and MANOVA?

My primary question is how to interpret the output (coefficients, F, P) when conducting a Type I (sequential) ANOVA? My specific research problem is a bit more complex, so I will break my example ...
17
votes
1answer
5k views

Goodness of fit and which model to choose linear regression or Poisson

I need some advice regarding two main dilemmas in my research, which is a case study of 3 big pharmaceuticals and innovation. Number of patents per year is the dependent variable. My questions are ...
465
votes
10answers
278k views

What is the difference between “likelihood” and “probability”?

The wikipedia page claims that likelihood and probability are distinct concepts. In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a ...
167
votes
4answers
246k views

How to interpret a QQ plot

I am working with a small dataset (21 observations) and have the following normal QQ plot in R: Seeing that the plot does not support normality, what could I infer about the underlying distribution? ...
63
votes
4answers
27k views

How can adding a 2nd IV make the 1st IV significant?

I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out. I have a least squares regression model, with one independent variable and one ...
154
votes
3answers
72k views

R's lmer cheat sheet

There's a lot of discussion going on on this forum about the proper way to specify various hierarchical models using lmer. I thought it would be great to have all ...
73
votes
3answers
16k views

Why isn't Logistic Regression called Logistic Classification?

Since Logistic Regression is a statistical classification model dealing with categorical dependent variables, why isn't it called Logistic Classification? Shouldn't the "Regression" name be reserved ...
231
votes
2answers
162k views

Interpretation of R's lm() output

The help pages in R assume I know what those numbers mean, but I don't. I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. ...
29
votes
3answers
22k views

Interpretation of simple predictions to odds ratios in logistic regression

I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between my interpretations of the following values which I thought would be the same: exponentiated beta values ...
415
votes
11answers
469k views

What is the difference between test set and validation set?

I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts: training set validation set test set I notice in many training or learning ...

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