# 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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### Correlations with unordered categorical variables

I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical. I'm looking for associations between these variables. I've been ...
39k 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 ...
178k views

### Correlation between a nominal (IV) and a continuous (DV) variable

I have a nominal variable (different topics of conversation, coded as topic0=0 etc) and a number of scale variables (DV) such as the length of a conversation. How can I derive correlations between ...
1.1m views

### What is the difference between discrete data and continuous data?

What is the difference between discrete data and continuous data?
49k views

### Does it ever make sense to treat categorical data as continuous?

In answering this question on discrete and continuous data I glibly asserted that it rarely makes sense to treat categorical data as continuous. On the face of it that seems self-evident, but ...
49k views

### Clustering a dataset with both discrete and continuous variables

I have a dataset X which has 10 dimensions, 4 of which are discrete values. In fact, those 4 discrete variables are ordinal, i.e. a higher value implies a higher/better semantic. 2 of these discrete ...
67k views

### Predicting with both continuous and categorical features

Some predictive modeling techniques are more designed for handling continuous predictors, while others are better for handling categorical or discrete variables. Of course there exist techniques to ...
5k views

### Continuous generalization of the negative binomial distribution

Negative binomial (NB) distribution is defined on non-negative integers and has probability mass function$$f(k;r,p)={\binom {k+r-1}{k}}p^{k}(1-p)^{r}.$$ Does it make sense to consider a continuous ...
10k views

### When should we discretize/bin continuous independent variables/features and when should not?

When should we discretize/bin independent variables/features and when should not? My attempts to answer the question: In general, we should not bin, because binning will lose information. Binning is ...
4k views

### Uniform random variable as sum of two random variables

Taken from Grimmet and Stirzaker: Show that it cannot be the case that $U=X+Y$ where $U$ is uniformly distributed on [0,1] and $X$ and $Y$ are independent and identically distributed. You should not ...
3k views

### Why is the Cauchy Distribution so useful?

Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
7k views

### $P[X=x]=0$ when $X$ is continuous variable

I know that for continuous variable $P[X=x]=0$. But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ?
25k views

### How to choose between ANOVA and ANCOVA in a designed experiment?

I am conducting an experiment which has the following: DV: Slice consumption (continuous or could be categorical) IV: Healthy message, unhealthy message, no message (control) (3 groups in which ...
19k views

### How to correctly assess the correlation between ordinal and a continuous variable?

I'd like to estimate the correlation between: An ordinal variable: subjects are asked to rate their preference for 6 types of fruit on a 1-5 scale (ranging from very disgusting to very tasty) On ...
17k views

### Correlation coefficient between a (non-dichotomous) nominal variable and a numeric (interval) or an ordinal variable

I've already read all the pages in this site trying to find the answer to my problem but no one seems to be the right one form me... First I explain you the kind of data I'm working with... Let's ...
2k views

### Computationally efficient estimation of multivariate mode

Short version: What's the most computationally efficient method of estimating the mode of a multidimensional data set, sampled from a continuous distribution? Long version: I've got a data set that I ...
1k views

### Is going from continuous data to categorical always wrong?

When I read about how to setup your data, one thing I have often come across is that transforming some continuous data into categorical data is not a good idea, since you may very well make the wrong ...
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### Analogues of sensitivity and specificity for continuous outcomes

How can I calculate the sensitivity and specificity (or analogous measures) of a continuous diagnostic test in predicting a continuous outcome (e.g., blood pressure) without dichotomizing the outcome? ...
3k views

### Clustering data that has mixture of continuous and categorical variables

I have data that represent some aspect of human behavior. I want to cluster it (unsupervised) into behavioral profiles of some sort. now, some of my variables are categorical (with 2 or more ...
861 views

### Correlating continuous clinical variables and gene expression data

In SVM (linear kernel) classification analyses of a data-set of gene expression (~400 variables/genes) for ~25 each of cases and controls, I find that the gene expression-based classifiers have very ...
10k views

### Calculating PDF given CDF

I know that the PDF is the first derivative of the CDF for a continuous random variable, and the difference for a discrete random variable. However, I would like to know why this is, why are there ...
10k views

### Integer Data: Categorical or Continuous?

I am wondering if integer predictor data should be treated as categorical (thus requiring encoding) or continuous. For example, if the range of a given predictor X ...
2k views

### Incremental training of Neural Networks

Is it valid to train a neural network over and over again with new arriving data (including pruning after each new training)? I plan to collect data for a period of time, train/cv/test the networ, ...
2k views

### 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. ...
3k views

### GLM with logit link and Gaussian family to predict a continuous DV between 0 and 1

Can you run a GLM using a logit link with a continuous DV (between 0 and 1)? Generally it's suggested to use a binomial family with a logit link, but I'm guessing that is because the model assumes a ...
6k views

### What is the best way to discretize a 1D continuous random variable?

Say I have a 1-dimensional continuous random variable $X$, with PDF $f(X)$, CDF $F(X)$ and inverse CDF $F^{-1}$. What is the best way to discretize $X$? To keep things clear, let $Y$ denote the ...
285 views

### How can I demonstrate non-linearity without categorising a predictor?

I don't know what is the appropriate term for my question. The scenario is described as following. In the analysis there one dependent variable Y and two independent variable X1 and X2. All three ...
1k views

### What to do with almost-continuous variable in regression?

I've been taught that binning a continuous variable into categories is almost never a good idea, because you lose information in the process. But now I'm facing a situation where I have an age ...