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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1answer
67 views

How is this connection between Beta and Binomial possible?

I'm learning stats, and I've reasoned about this for many days and I'm losing sleep over it. Say I have a binomial distribution B(k; n, p) simulating a hypothesis <...
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895 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/...
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13 views

Transforming data with a range of values

What is the best way to compute descriptive statistics from a wage_range variable collected as follows and use it for OLS purposes or should this variable be completely ignored from empirical analyses:...
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12 views

Converting continuous predictor to category e.g. Age [duplicate]

I notice that on many examples one is keen to convert Age to a categorical age range. I am wondering if that is always necessary. The famous golf play decision tree example has ranges for temperatures ...
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9 views

Excel NORM.DIST() calculation for a specific value of x (CUMULATIVE = FALSE)? [duplicate]

We know that the value of PDF at a specific time (X = x) is 0 due to the nature of a distribution of a continuous variable. However, I noticed that when I plug in some test numbers in NORM.DIST() in ...
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1answer
84 views

How should one understand Bayes theorem with probability distributions?

I'm learning about VAEs, and need to go this deep to understand them. However, the question is for Bayes theorem with probability distributions. I learnt about Bayes theorem from this video. Excellent ...
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2answers
54 views

If $X$ is a continuous random variable with support $A$, does this imply that the cdf of $X$ is strictly increasing on $A$?

If $X$ is a continuous random variable with support $A$, does this imply that the cdf of $X$ is strictly increasing on $A$? My guess is yes. But just in case, let me know if you can think of any ...
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41 views

Modeling covariates in multiple regression

My aim is to find the association between intake of chocolate (continuous predictor) and blood pressure (continuous outcome) in a multiple linear regression. I have to include many covariates in order ...
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Doubt on regression analysis interpretation

I have a dataset made of more than 10K observations. For each of them I know the value of a continuous variable (C1), and the value of three nominal variables: N1, which can take three different ...
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40 views

How to interpret crossover-interaction between continuous and categorical variable?

I am stuck with the interpretation of my model results. In the beginning I have tested my independent variables for correlation with Theil's U and left out correlated ones to avoid multicollinearity. ...
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18 views

Do I have to apply the same kind of transformation and scaling to all data? [duplicate]

I'm new to machine learning and currently learning it, and I do not quite understand the topic of continuous data transformations for machine learning. If I have 6 pandas columns of continuous data, ...
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5 views

What analysis should I use for longitudinal (observational) data with continuous IV and DV?

I collected data from the same participants twice over two weeks (time 1 and 2 are two weeks apart). Between time 1 and time 2 there was a significant event, which we hypothesized, would've changed ...
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How to model zero-inflated continous (from negative to positive) data

We have a dataset of around 20k observations. The dependent variable is the change (i.e. delta) on the amount of a common resource (e.g. land) of individual households in a year, so: It has negative ...
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12 views

Probability of intersection involving a continuum

I'm trying to derive pascal's rule of succession that I saw on a 3b1b video in a rigorous-like way(i don't have a solid background in measure theory so I can't pretend to be rigorous). let $ ω=[0,1] × ...
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45 views

Likelihood of Gaussian Process for continuous data

I need to calculate the likelihood $L(\theta)$ of the Gaussian process: $ y(t) \sim GP(m(t), K((t,t')|\theta)) $ where $m(t)$ is the mean function (this will be zero for my purposes) and $K((t,t')|\...
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In real-life applications, which continuous distributions have NON-CONVERGENT expectations that require Lebesgue integration?

When computing expected values, Riemann integration works for only random variables with bounded support sets. For distributions with unbounded support sets, we can use improper Riemann integrals for &...
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1answer
22 views

Variable data measured discretely with poor resolution

Is there an appropriate method for estimating variation when variable data is measured discretely where the resolution is poor. Here's an example: You are looking at how long it takes for a solid to ...
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1answer
14 views

How to decide whether to use regression or classification model?

I just started machine learning , and I was confused about which model to use, regression or classification , when we have a target variable like age or a variable like movie rating , which may have ...
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38 views

Latent Profile Analysis in R with continuous and categorical variables

I am trying to do an LPA with categorical and continuous variables. The tidyLPA package is amazing for continuous variables but models don't seem to converge with categorical variables, and the ...
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0answers
24 views

Represent Integer Categorical feature as both Numeric and Categorical

I'm dealing with tabular datasets where it's really hard to tell if the integer column is Numeric or Categorical. My main consideration is the accuracy of the model that I am building (no deep ...
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22 views

Analysis of One Binary Variable and Continuous Variables - Ecological Data

I have a dataset that I am trying to analyse, it consists of: A binary variable which indicates a tree species (0 = deciduous 1 = evergreen) with 100 measurements each. N which is leaf nitrogen ...
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1answer
87 views

How to compute the median of a continuous distribution?

I don't have a solid background in statistics so the concept of probability density functions in the statistics course I'm taking is new to me. I need to derive the median of a continuous distribution ...
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1answer
27 views

In practice, how to discretize continuous regressor with minimal impact on coefficient (or minimal information loss)?

Suppose I have some continuous data that looks like this (this is a mini example, not my real data): ...
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1answer
22 views

Are zero inflated models appropriate if the predictor/x variable is the one that is zero-inflated?

As the title suggests. I was under the impression that zero-inflated models are generally used when zero values are over-represented among the response/y variables, but now I am dealing with a ...
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22 views

Multivariate Regression: Both Continuous and Categorical Predictor Variables

I am involved in a meta-analysis assessing the role of multiple baseline characteristics (e.g. age, BMI, symptoms and signs) in a given disease. One element of our analysis includes a multivariate ...
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9 views

What's the good way to find outliers in the continuous physical process measurements time-series? (picture attached) [duplicate]

What's the best way to find outliers in the time-series like the one attached? Just using the knowledge that it is a measurement of a continuous physical process. The data is quite short (200-500 ...
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1answer
28 views

Can we normalize both continuous and discrete numerical values

I have a sensor dataset with 16 features as numerical values (12 are continuous and 4 are discrete). I am using LSTM model to fit the data and do some classification. As both continuous and discrete ...
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1answer
101 views

How to estimate the optimal cutpoint for a binary outcome in python?

I have a dataset of diabetic patients which has been used to train an xgboost model in several outcomes such as stroke, amputation, and more. Originally we used the continuous numeric variables as-is, ...
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1answer
65 views

What's the best way to find outliers in the time-series, encountering that it is a real-world mechanical process (process continuity)?

What's the best way to find outliers in the time-series, encountering continuity? I attached two time-series that I'm interested to filter. One is less noisy, and one is a bit noisier. I'm mostly ...
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22 views

Interpreting logistic mixed model estimates of a model with continuous and categorical predictors

Newbie here. Sorry in advance if I express poorly as I don't completely master yet the vocabulary of statistics! I am performing a logisctic mixed model - with glmer - which presents as follows: CE ~ ...
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13 views

creating a continuous variable from ordinal variables

Could I simply sum up ordinal variables (some 4-,some 7-scale) to create a continuous dummy variable, and include it in a regression model? E.g. ...
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1answer
31 views

Stratify Cox Proportional Hazard Model on continuous variable

I have a question regarding Cox proportional hazard models. I've been working with data with some time-varying variables and some that are fixed over time. In total 79 units are surveyed giving around ...
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1answer
35 views

Years as continuous variable [duplicate]

Can I use "years" as a continuous variable ("years" as calendar years from 1984 to 2014) to see if NDVI (normalized difference vegetation index), of the same area at the same time (...
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1answer
56 views

Positive or negatively bounded CDFs [closed]

If $X\in\mathbb{R}^n$ is a continuous random variable whose cumulative distribution function is ordinarily $$F_X(x) = \int_{-\infty}^{\infty} f_X(x) dx $$ what is the meaning of $$F_X(x) = \int_{0}^{\...
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15 views

How to conduct meta-regression with a continuous variable measured on different scales across studies?

I am conducting a meta-analysis on the efficacy of a specific type of psychotherapy for children and plan to use meta-regression to identify moderators. The predictor I am interested in is parent ...
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2answers
78 views

Sample size calculation for linear regression model with random intercept

I am trying to calculate the sample size for a mixed linear regression model. The dependent variable is continuous and the model includes 2 further continuous variables. The random intercept is based ...
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0answers
32 views

Deriving comparable probabilites from continuous and discrete data

I'm creating an elections index that's adjusted by how close the results are expected to be for a number of upcoming races in the US. My simulated results include discrete values like seat counts for ...
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1answer
20 views

Summarizing Likert-type Data

I used a questionnaire with several questions on a five point scale (never, rarely, sometimes, often, always) to determine how well a person liked their job. I then assessed the average scores for ...
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0answers
34 views

correlation between a continuous and a binary variable [duplicate]

I am interested between the correlation between a continuous variable and a binary variable (female=1/male=2). I think it doesn't really make sense to calculate it like this: ...
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1answer
2k views

How to check the correlation between categorical and numeric independent variable in R? [duplicate]

Just wondering if i need to check correlation between categorical and numeric independent variable in R, is there any specific package available in R. Or should i just find the correlation between the ...
10
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1answer
674 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 ...
2
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1answer
25 views

Use different Naive Bayes classifiers to target different data

I am practicing using the Naive Bayes classifier to predict whether people get a stroke or not, but, I am confused with two classifiers. One is categorical Naive Bayes, another is Gaussian Naive Bayes....
2
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1answer
28 views

Does a random variable's distribution also carry over to its histogram-estimated probabilities?

If I have a finite sample of a continuous random variable $x$ as a vector containing $N$ observations, then I bucket those observations based on their frequency of appearance into equally-sized bins ...
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8 views

Mixed design with continuous between participants measure

Context: I commonly used mixed factorial designs that consist of two of more repeated-measures factors, that participants experience within the same experimental session, and a between-participants ...
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2answers
146 views

Do financial return series have a probability mass function (pmf)?

Stock returns, computed from stock prices as $r_t = \ln (p_{t}) - \ln (p_{t-1})$, are real-valued and unbounded giving the impression that they are continuous random variables. But aren't they ...
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1answer
86 views

multiple regression with continuous and binary regressors

How can I do a multiple regression if I have continuous and ordinal (binary) (eg. male and female) regressors. Can I just add them like this lm(y~x1+x2+x3+x4, data=data)?
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1answer
28 views

Gaussian Mixture Model $p(x_i | z_i = k)$ a likelihood or probability?

In Gaussian Mixture models, the probability of observing the data $x$ given that it was generated from $M$ gaussian models is given by the following equation $$p(x) = \sum_{k=1}^m p(x|z=k)p(z = k)$$ ...
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33 views

Why do continuous data distributions have entropy of negative infinity?

Entropy is intended for discrete random variables, while differential entropy is used on continuous r.v.'s. This question is the opposite of another similarly titled question about discrete data and ...
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1answer
259 views

GLMM hurdle model for continuous data -Truncated negative binomial family in glmmTMB?

I am running a hurdle model using the glmmTMB function. My dependent variable is continuous and >= 0. I was looking for a function that would allow me to model the binary response in a logistic ...
2
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1answer
42 views

Is a bounded real-number random variable discrete or continuous?

A discrete random variable is countable (such as integers and natural numbers), whereas a continuous r.v. is not countable (like the real numbers $\mathbb{R}$). If I have a dataset whose observations ...

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