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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137
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6answers
264k views

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 ...
95
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8answers
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 ...
89
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1answer
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 ...
73
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10answers
1.1m views

What is the difference between discrete data and continuous data?

What is the difference between discrete data and continuous data?
59
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8answers
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 ...
35
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5answers
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 ...
30
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4answers
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 ...
28
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2answers
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 ...
27
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2answers
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 ...
22
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2answers
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 ...
18
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2answers
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?
18
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4answers
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 ?
17
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1answer
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 ...
17
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2answers
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 ...
15
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2answers
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 ...
15
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3answers
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 ...
14
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2answers
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 ...
14
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3answers
2k views

Conditional probability of continuous variable

Suppose that random variable $U$ follows a continuous Uniform distribution with parameters 0 and 10 (i.e. $U \sim \rm{U}(0,10)$ ) Now let's denote A the event that $U$ = 5 and B the event that $...
13
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5answers
5k views

Why should binning be avoided at all costs?

So I've read a few posts about why binning should always be avoided. A popular reference for that claim being this link. The main getaway being that the binning points (or cutpoints) are rather ...
13
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1answer
28k views

How to test if my data is discrete or continuous?

It seems to me that to choose the right statistical tools, I have to firstly identify if my dataset is discrete or continuous. Could you mind to teach me how can I test whether the data is discrete ...
12
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2answers
26k views

Correlation between dichotomous and continuous variable

I am trying to find the correlation between a dichotomous and a continuous variable. From my ground work on this I found that I have to use independent t-test and the precondition for it is that the ...
12
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3answers
48k views

Can I use multiple regression when I have mixed categorical and continuous predictors?

It looks like you can use coding for one categorical variable, but I have two categorical and one continuous predictor variable. Can i use multiple regression for this in SPSS and if so how? thanks!
11
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2answers
12k views

Using poisson regression for continuous data?

Can the poisson distribution be used to analyze continuous data as well as discrete data? I have a few data sets where response variables are continuous, but resemble a poisson distribution rather ...
11
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3answers
20k views

How to interpret a hazard ratio from a continuous variable — unit of difference?

I am reading an article which shows Hazard Ratios for continuous variables, but I'm not sure how to interpret the given values. My current understanding of hazard ratios is that the number ...
11
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5answers
3k views

Probability that a continuous random variable assumes a fixed point

I'm in an introductory statistics class in which the probability density function for continuous random variables has been defined as $P\left\{X\in B\right\}=\int_B f\left(x\right)dx$. I understand ...
11
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1answer
2k views

Determining an optimal discretization of data from a continuous distribution

Suppose you have a data set $Y_{1}, ..., Y_{n}$ from a continuous distribution with density $p(y)$ supported on $[0,1]$ that is not known, but $n$ is pretty large so a kernel density (for example) ...
10
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1answer
737 views

Why is measure theory needed to understand continuous random variables and probability density functions in particular?

Prefacing the question with the fact that I have no knowledge of measure theory. I would prefer a conceptual answer, as there already many mathematical ones. Also, why don't we need measure theory to ...
10
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1answer
940 views

Why the sum of two absolutely-continuous random variables isn't necessarily absolutely continuous?

Why "a sum of two absolutely-continuous random variables does not need to be absolutely continuous"? See problem 6.4 on page 6 in https://web.ma.utexas.edu/users/gordanz/notes/...
10
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1answer
357 views

Is it ever a good idea to give “partial credit” (continuous outcome) in training a logistic regression?

I am training a logistic regression to predict which runners are most likely to finish a grueling endurance race. Very few runners complete this race, so I have severe class imbalance and a small ...
9
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3answers
12k views

How can the probability of each point be zero in continuous random variable? [duplicate]

I know this is duplicated but I think the question is a bit different and needs different answer. How can CDF be continuous and have derivative at each point that is not equal to zero but the ...
9
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2answers
7k views

Common Continuous Distributions with [0,1] support

Question I am looking to understand what possible common statistical continuous distributions exist with support [0,1]. Background In my work I often come across data which are bounded between 0 and ...
9
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2answers
15k views

How do you plot an interaction between a factor and a continous covariate?

I would like to plot on the same graph the interaction between my continuous predictor and my categorical moderator. I know how to do it when both are categorical (factor interaction), but don't ...
9
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2answers
480 views

Best practices when treating range data as continuous

I am looking at whether abundance is related to size. Size is (of course) continuous, however, abundance is recorded on a scale such that ...
9
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1answer
2k views

Why reducing a regression model into a classification model by output discretization improves a model?

In regression problems, if the output is discretized into bins/categories/clusters and used as labels, the model is reduced to a classification model. My question is: what is the theoretical or ...
9
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3answers
9k views

Can random effects apply only to categorical variables?

This questions might sound stupid, but... is it correct that random effects could apply only to categorical variables (like individual id, population id, ...), e.g. say $x_i$ is categorical variable: ...
9
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2answers
18k views

Continuous and Categorical variable data analysis

I have three variables: distance (continuous, variable range negative infinity to positive infinity) isLand (discrete categorical/ Boolean, variable range 1 or 0) occupants (discrete categorical, ...
9
votes
3answers
300 views

For a continuous random variable, why does $P(a < Z < b) = P(a \leq Z < b) = P(a < Z \leq b) = P(a \leq Z \leq b)$

My textbook puts this in a sidebox with the heading "Note" and doesn't explain why. Could you tell me why this statement holds? $P(a < Z < b) = P(a \leq Z < b) = P(a < Z \leq b) = P(a \...
9
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3answers
4k views

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? ...
9
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2answers
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 ...
9
votes
1answer
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 ...
8
votes
4answers
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 ...
8
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3answers
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 ...
8
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2answers
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, ...
8
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1answer
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. ...
7
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3answers
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 ...
7
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2answers
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 ...
7
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2answers
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 ...
7
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3answers
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 ...
7
votes
2answers
2k views

Regression Using Continuous Variable with Nulls

I'm in a bit of a quandry with a logistic model I'm working on. As one of the explanatory variables, I want to include "Days since last visit" (or some transformation of it), however about 20% of the ...
7
votes
1answer
3k views

Regression random forest and highly skewed response distribution

There is a great deal of information on how unbalanced data sets may impact predictive accuracy in classification problems. Several solutions have been proposed (see here). My questions are: Can a ...

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