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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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 ...
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 ...
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 ...
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 ?
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 ...
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 ...
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 ...
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 ...
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?
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 ...
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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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 ...
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 ...
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 ...
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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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) ...
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 ...
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 ...
5
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1answer
3k views

How to interpret interaction continuous variables in logistic regression?

I am struggling to understand and interpret the interaction term in a logistic regression. The explanatory variables are temperature (categorical), ...
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1answer
1k views

Analyzing relationships between ordinal and continuous time series data

I have two sets of time series data - roleTrajectories & normalizedDegree. The former data set contains ordinal rankings of subjects' positions within a network at 13 time periods. The latter data ...
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 ...
3
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1answer
1k views

Beta regression with “random effect” of source plot in two seasons

I am attempting to model the effect of several continuous and categorical predictors on a continuous proportion response variable. My experiment had 3 treatments, which were replicated in each of 9 ...
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 ...
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 ...
6
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1answer
4k views

Rank transformed 2-way ANOVA

I know I'm asking a lot of questions these days! Sorry about that, but I'm trying to work through my grad thesis data collected over the last 4 years, and am repeatedly tripping on my beginner's grasp ...
6
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1answer
6k views

How to transform continuous data with extreme bimodal distribution

Is there a way to transform a continuous predictor variable (grant) that has a bimodal distribution into a normal distribution (see density plot below)? I have tried log(x+c), z-score and inverse ...
3
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1answer
191 views

Different Types of Data

According to my Elementary statistics for Business and Economics text book revised Edition 2012 . Under a section concerning the Different types of Data . This text book says that under Quantitative ...
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2answers
505 views

Expectation of 2 functions with one random variable

This may be a trivial question but I want to consult with you all. Let U be a continuous random variable taking values int he interval [0,2pi]. Let X = cos(U), Y = sin(U). Determine the Pearson ...
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?
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, ...
1
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2answers
472 views

Measure of association between non-dichotomous ordinal variable and continuous variable

I have to collect and then analyse a large dataset. A particular data input (continuous variable) is laborious to collect and I believe that an ordinal category (1,2,3,4) would correlate closely with ...
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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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? ...
4
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1answer
1k views

Why X=x is impossible for continuous random variables?

Background: When we consider a continuous random variable $X$ and consider some independent realisations of $X$, I am told that the realisations must be unique since $\text{Pr}(X=x)=0$. When we ...
2
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1answer
2k views

hurdle model with non-zero gaussian distribution in R

I have biomass data (continuous response variable). If sufficient data is collected, the log(Biomass) follows a normal distribution. However, I am separating the overall biomass by family (i.e., ...
1
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1answer
518 views

how to measure the correlation between non-normally distributed numeric variable and nominal variable?

I have two nominal variables and some numeric variables. The first nominal variable is a binary one. I want to measure the correlation between this binary variable and the other numeric variables. ...
3
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2answers
498 views

Gibbs sampling and mixed distribution

For a project, I need to simulate from a joint distribution with both continuous and discrete variables that are dependent. The conditional distribution of any variable given the rest is known. I ...
2
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1answer
313 views

Transforming continuous variable to ordinal for estimation with ordered logit

I currently have a continuous variable. However, I would like to transform it into 5 intervals using cutpoints of my choosing to carry out an ordered logit estimation. That is: Will this affect the ...
1
vote
1answer
403 views

Using counts of a continuous random variable to establish an unknown probability density function

The precision of a given measuring device defines a window over the probability density function of whatever is being measured. For instance, if a measuring tape is precise to 0.1 inches, then the ...
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 ...
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 $...
4
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1answer
21k views

ANOVA or Regression? 1 Continuous factor & 1 Categorical factor with continuous response variables

I have 1 categorical factor (3 treatments) and 1 continuous factor (weight) and then I have 5 continuous response variables. From what I have read, I should not use a two way ANOVA as one of the ...
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: ...
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 ...
4
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2answers
20k views

interaction of categorical and continuous variables

I have a dependent variable that is continuous and I have two independent variables: one continuous and one categorical (with 2 categories) The interaction between the independent variables is ...
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 ...
3
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1answer
11k views

Correct glmer distribution family and link for a continuous zero-inflated data set

Data set details: Zeros are "real" (volume) Data set is heavily left skewed (even when zeros are excluded) Response is continuous (volume) Can anyone recommend a distribution family and link that I ...
6
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5answers
2k views

Clustering of variables: but they are mixed type, some are numeric, some are categorical

I have a dataset with 15 variables. Some variables are numeric, continuous. Other variables are boolean, dichotomous (true/false). There's also one variable categorical, nominal. ...
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 ...