Questions tagged [continuous-data]

A random variable $X$ is called continuous if its set of possible values is uncountable, and the chance that it takes any particular value is zero ($\text{P}(X = x) = 0$ for every real number $x$). A random variable is continuous if and only if its cumulative probability distribution function is a continuous function.

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Feature selection using chi squared for continuous features

I'm looking at univariate feature selection. A method that is often described, is to look at the p-values for a $\chi^2$-test. However, I'm confused as to how this works for continuous variables. 1. ...
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Identifying non-linearities in relationship between variables

Logistic regression is often used to identify the effect of $x$ on a binary variable $y$ after adjusting for potential confounders $x_1,...,x_n$. In the medical literature, I will sometimes encounter ...
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Truncated Explanatory Variable

I am running a model where one of the explanatory variables is truncated. In particular, the variable measures the duration of unemployment (retrospectively) in months and it is truncated at 2 years, ...
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244 views

Books for mixed distributions (continuous and discrete)?

What is a good book that covers mixed distributions? Most statistics books either only briefly mention them or do not cover the topic at all. I'd like to have a comprehensive resource covering ...
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Autoencoder with Mixed Data

Is it reasonable? The categorical features can be binary ("true" or "false") or strings, which are one-hot encoded. Some continuous features may be integers, which are treated as real values. If an ...
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208 views

How to estimate a continuous analog of the (discrete) vector autoregression (VAR) model

I have some ten to 100 thousand observations on each of around 500 entities. I have good reason to believe that these observations all mutually influence one another, in possibly complicated ways, or ...
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91 views

Estimating a probability distribution with a discrete and continuous part

This is a question more for advice and a suggested starting point than anything else (though anything else is cool as well ) The data that I have is something like this - 1,000,000 data points of ...
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95 views

What are best practices for visualizing/selecting visualizations for continuous data?

There appear to be a large number of rules of thumb for histogram bin size and kernel selection for density plots. Are histograms and/or density plots really the best visualization for a single ...
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125 views

Splitting a variable with nominal and numeric values

I have a variable that has both numeric and nominal components. The source has a documentation which helps in identifying which is which and for splitting into their proper components. I will do ...
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503 views

Testing if treating a categorical variable as continuous is okay

Pardon me if this is a simple question, but I haven't found a great resource for this just yet. Yes, I know that when possible, we should try to treat ordinal variables as categorical rather than ...
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277 views

Dependent variable maximum value contingent on independent variable

I am trying to create a model for debt collections. In the past I have used logistic regression to predict pay/no-pay. This has worked well but has a few unfortunate consequences. People are more ...
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1answer
12k views

How to analyse a continuous response having a bimodal distribution?

I am investigating unconscious racial prejudice as a predictor for guilty or not guilty judgements (Using SPSS). I have a continuous variable for unconscious racial prejudice (higher numbers equal ...
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399 views

Is continuous mutual information the correct analogue of the discrete version?

I'm interested in the mutual information of two continuous random variables $X$ and $Y$. Shannon defined differential entropy as $h(X) = -\int p_X(x)\log p_X(x) dx$, where $p_X$ is the probability ...
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36 views

What is the most appropriate way to compare means when group size is markedly different?

This scenario seems to be arising more and more with the usage of large datasets in an attempt to identify pilot data for associations, etc. I'm trying to figure out what method - if any - is the most ...
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125 views

Correlation analysis on two different groups of continuous heterogeneous variables with different range/scales in R

I would like to perform in R a initial simple correlation analysis, between a gene signature that i have identified, and some continuous clinical parameters, measured on the same patients, to identify ...
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185 views

Family distribution for continuous count data

I need to model the variable Total motile Count which describe how many million sperm cells in an entire ejaculate are motile. It is not a proper count since it is calculated as a product of other ...
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396 views

Discretization of a continuous distribution

I have two variation of the same problem. A) Assume you sample $m$ points, $x_1,x_2,...x_m$, drawn i.i.d from a continuous distribution of a random variable $X$. We reorder the points so $x_1<x_2&...
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How to calculate odds ratio per unit decrease of continuous variable

I have a logistic regression model obtained in R comparing association between two index diagnoses (0 or 1) with Age (continuous) + ...
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63 views

What is the best way to simultaneously fit multiple binomial and continuous predictors?

What is the most efficient way to fit a linear model w so that Y = w . X, where X is a ...
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208 views

Confidence-interval of continuous-Poisson distribution

I have searched the state of the art of continuous-Poisson distribution [1](normally known as) \begin{align} f(k,\lambda) = \frac{\lambda^k e^{-\lambda}}{\Gamma(k+1)},\lambda\in R^+, k\in (-1,\infty) \...
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84 views

Continuous dependent variable that almost looks like a categorical variable

I recently conducted an experiment where people had to decide how much money to take from another participant. People could choose to pick any value between 0 and 100 percent. It turns out that around ...
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669 views

Using controls as basis for quantile/tertile categorization

I have a number of continuous but really skewed variables in the statistical analyses I am currently performing. Even though I am strongly in favour of keeping them just as they are and relaxing ...
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469 views

Averaged continuous Kernel Density Estimates in lieu of a discrete Kernel Density Estimate in Monte Carlo Proceedure

I am thinking of using this code in a Monte Carlo routine to generate Kernel Density Estimates for subsequent use in a Naive Bayes Classifier (see this earlier post). The author of the code states ...
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What happens if validation/real data has values outside training set limits for continuous data?

Describing Example: If feature X1 in training data has values inside [0,1] However, X1 in real/validation data has values [-1, 2[ What happens then? Previously discussed On previous discussions with ...
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How to deal with ties to fit data into continuous distributions in R?

I have rainfall duration and volume data. the duration is ...
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1answer
31 views

How can I compare the predictive power or association of two variables of different nature?

I am dealing with the following problem: We have 3 variables: A continuous variable (0 to 1), that is a scoring for people. A discrete variable, offered by a partner, in the range 1..10. That is also ...
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33 views

Bivariate copula for count and continuous variables?

I'm interested in fit a Copula from my bivariate data with a count variable $Y_{i}$ and a continuous one $X_{i}$. So, let $F(x)$ and $G(x)$ be the margins for the mentioned variables and $C$ the ...
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178 views

How to compute and interpret interaction term between continuous variables that have negative values?

I was wondering about the computation and interpretation of interaction terms of continuous variables that are used in a multiple regression. Normally, one would mean-center (or z-standardize) the two ...
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2answers
385 views

What is between regression and ordinal classification (or called ordinal regression)?

There are many articles explaining the difference between regression and ordinal classification, most of them mentioned that regression is for continuous response while ordinal classification is for ...
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47 views

Why does rank correlation only depend on copula, and not on the margins, if the margins are continuous

I read that for continuous margins, then Rank correlation only depend on copula and not on the margins. However, it is not the case for the non-continuous margins. Is that because the Kendall's tau (...
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302 views

Calculating variance and standard deviation of continuous time series

I am trying to calculate the variance and standard deviation of an unevenly spaced continuous time series. Example data: ...
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63 views

Mutual information between continuous $Z$ and $g(Z)$ for differentiable $g$?

I have a continuous random variable $Z$ and a differentiable function $X = g(Z)$. Is the mutual information between $X$ and $Z$ necessarily $\infty$ or 0? Are there any examples of differentiable ...
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1answer
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Interpreting effects of categorical and continuous predictors in multiple linear mixed models

I'm building a LMM model with a continuous DV (signal amplitude) and two IV: one continuous (questionnaire score) and one categorical with 3 levels (condition). Conditions are: S, M and SM (the last ...
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140 views

Categorizing continuous response variables: good or bad?

I have two continuous variables that I wanted to model on 5 explanatory variables. When I did, using linear regression (and mixed-effects linear regression), none of the variables were statistically ...
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634 views

Does the integral of the probability density function squared mean something?

I've been searching but I couldn't find on the internet if there's any significance for the integral of the pdf squared: $\int_\mathbb{R} f^2(x)$ That's because, as an alternative of Shannon entropy,...
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1answer
57 views

Estimating the likelihood of an observed path for a continuous state space Markov process

Problem statement Let $\mathbb{X} \subset \mathbb{R}^{k}$ and let $p:\mathbb{X}\times\mathbb{X}\rightarrow\mathbb{R}$ be a density kernel on $\mathbb{X}$. We assume the following model for the ...
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569 views

Is there a way to automatically detect if a variable is multiple categorical or continuous

If your dataset is big, say you have thousands of variables. Some variables are multiple categorical and some are continuous. Question is, how do you know if a variable is continuous vs multiple ...
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56 views

Moving from discrete sum of changes to continuous integral of local covariance - how is this done?

I'm trying to derive a specific relationship about the relationship between forwards and futures. The expression is from the paper, "The relationship between forward and futures prices", written 1981 ...
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61 views

Continuous entropy comparison

I have a continuos time signal (speech signal) and I will add noise to it at different SNRs. I want to compare the entropy or the original signal (clean speech) with the noisy ones. The idea is to ...
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46 views

Finding an MLE fit when a model predicts two kinds of data, each with a different distribution / data model

My problem is as follows: I am fitting some multi-parameter models which predict two different kinds of data. I can find a best (MLE) fit to the first kind of data. I'm currently expressing both the ...
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212 views

Mean First Passage Time (MFPT) of CTMC

Could anyone possibly advise me on how one would go about calculating the MFPT matrix of a continuous-time Markov chain? I've tried looking around online, but I can only find information on discrete-...
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346 views

How to set sum contrasts for unbalanced factors

Let's say that I have a model where the response time depends on accuracy (0/1, coded either as categorical or numerical) and another categorical variable (pres: idem/diff), both interacting with the ...
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463 views

Interpretation of continuous by continuous interaction in binary regression model

I'm performing binary logistic regression in SPSS; y is dichotomous variable; and both Xs are continuous variables. I performed three models and I have troubles interpreting model with both ...
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53 views

The marginal likelihood of a fully-observed continuous time Markov chain

Say we have a fully observed trajectory $S$ from a CTMC. For a generator/rate matrix $Q$, we place gamma priors $\mathrm{Gamma}(\alpha_{1},\alpha_{2})$ on the diagonals, and $\mathrm{Dirichlet}(\beta)...
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Regression modelling with mixed data set: categorical and numerical predictor variables

There are thirteen predictor variables which are a combination of 8 continuous, 4 binary and 1 categorical variables. The dependent variable is again categorical. I understand that I need to use dummy ...
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147 views

Marginalizing multivariate-normal distribution canonical form

Regarding the problem of margenalization of canonical forms of multivariate gaussian distribution it was mentioned in probabilistic graphical models text book that $$\int{C(X,Y;k,h,g)}dY$$ is ...
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142 views

Unified Variable Classification

I am trying to go beyond Stevens' Level of Measurement Typology. Here is what I have so far: Discrete Variables Nominal (like Apple, Banana) Ordinal (like 1, 2, 3) Count (like 0, 1, 2) Incremental (...
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Why big difference between categorical and continous variable inregression analysis?

I am currently doing a survival analysis where I want to adjust for several confounders. One of my variables, which I will name MyScore is a score from 1-5. When I enter MyScore as a continuous ...
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1answer
145 views

Best method for predicting a numeric response from multiple proportional predictors?

I have some data where I want to predict a continuous, approximately normally distributed response/dependent variable with three predictors which are all proportions (i.e. 0-1). The three proportions ...
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134 views

How to test when the data is both binary and continuous?

I gave a recall test to the participants to examine the accuracy of their answers. I have one IV with two levels, present or absent. I have 11 DVs (questions in the exam), 4 of which are continuous (...

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