Questions tagged [errors-in-variables]
Errors in variables are measurement errors which increase the estimation variance (error in the dependent variable) or bias the regression coefficients towards zero (error in the independent variables).
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What happens when there are errors in the predictor variables?
I asked this question yesterday but I can't log into my account anymore: Using a Response Variable as a Predictor Variable in a Future Model?
After thinking about this question (estimate net cost-...
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Asymptotic Variance of the 'naive' estimator in measurement error model
Consider the classical measurement error model:
$$Y= \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \varepsilon$$
where $W=X+U$ is observed. X is the 'true' quantity and U is the measurement error. Var$(X) = \...
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Need help with propagation of errors
Let $v_i$ and $u_i$ be measured data and noiseless data respectively, where $i \in \{1, \ldots, N\}$ denotes the $i^{th}$ realization of the random variables $v$ and $u$. The random variables $v$ and $...
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What is a good introduction to errors-in-variables models?
I'm aware of this resource https://en.wikipedia.org/wiki/Errors-in-variables_models, but I don't put a lot of faith into wikipedia articles on stats, so I'm looking for some reliable references on the ...
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Is reduced major axis regression a special case of total least squares?
Edit: It seems the answer to my first question is that the website has a typo. $\lambda = V_{y}/V_{x}$, NOT $\lambda = V_{x}/V_{y}$. But I'm still stumped on the second question about why it cannot be ...
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What is the Likelihood Formula for an Error in Variable Model?
I am comparing different models ability to explain my joint observation of (X,Y) with AIC for which I need the likelihood.
How can I calculate the likelihood of (X,Y) for the error in variable model ...
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Asymmetric errors on cluster size distributions
I have a question that might seem simple, but I'm unsure how to address it.
For an analysis on pixel detectors, I am extracting a histogram similar to the ones attached, focusing on the cluster size ...
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Errors-in-variables regression with sample size weighting?
Very belated follow-up to a previous question:
I have some pretty simple linear models predicting a rate (continuous response var) from certain features of the distribution of some measured value. The ...
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A lot of variables in a Quadratic Discriminant Analysis
I'm trying to make a Quadratic Discriminant Analysis in R, but appears the follow mistake: "some group is too small for 'qda'". I was reading about it and I concluded that I have more ...
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Error-in-Variables regression p-value?
I ran an EIV model in r and I was wondering if there is something else besides the R-adjusted to see if the fit of the model is good?
I noticed that eivreg function ...
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Calculate the average of absolute values of a measurement with a measurement error
I have a few parameters; each is measured imprecisely with a known but unique random
measurement error. We can assume that the error is normally distributed, with mean 0 and known variance (different ...
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What is the best linear regression method when the errors in the variables x and y are unknown?
I have pairs of observations $(X_i,Y_i)$ with errors in both variables and I need to find the line that best fits the data. I have found some methods, but it is essential to know the standard ...
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Hypothesis testing using samples with different measurement errors/intervals
Are there generalizations of common hypothesis tests (e.g. t-test, mann-whitney) that can take into account different confidences in the sample measurements?
For example, if I have two sets of ...
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When calculating the statistical power of a t-test, do I need to consider the uncertainty of the single values?
I have a question regarding calculating the power for a statistical test that includes data which are estimated by a model (means they have an uncertainty):
I want to find out if two piles of stones ...
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Linear Regression but the Variables have errors
I have received this confusing task:
You have two variables 𝑥 and 𝑦, where y is a response variable which can be written as an explicit linear function of 𝑥. However, the technique used for ...
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What does Deming regression estimate?
Least squares regression estimates conditional means.
Least absolute regression estimates conditional medians.
Quantile regressions estimate conditional quantiles (a special case of which is the ...
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What is the name of this regression model?
I am wondering how I can map this problem to something known.
Let us start with a standard linear regression framework, and suppose we want to reconstruct an observed signal $y$ from single known ...
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How to test for correlated errors in regression
I understand that one assumption that must hold for regression is for there to be no correlation in the error structure.
Put another way:
The residuals should be impossible to predict above chance.
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How to compare distributions with errors on the data points?
Here's a mock set-up of my problem:
I have two non-normal probability density distributions (PDFs), $A$ and $B$.
Distribution $A$ has error measurements for each data point while distribution $B$ ...
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MLE on Structural VAR
I have a simple model that I wish to fit using data. The model is of the form below.
\begin{gather}
y_t = -\lambda r_t + \theta a_t + \varepsilon_1 \\ \\
\pi_t = \pi_{t-1} + w y_t + \varepsilon_2 \\ \\...
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Removing the bias from some unknown measurement error
Imagine I have two variables X and Y which have a statistical relationship. However I cannot observe X. I can only observe X* = X + U where U is some 0-centered random noise. I don't know U but I ...
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Linear least-square fitting of two variables with uncertainty on both
I am trying to find an R function to calculate the linear least-square fitting of two variables when both have an error (expressed as standard deviation). I have found this problem referred to in half ...
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Interview question (incomplete): extension of linear regression (errors in variable)
Here is a interview question I head from others, but I think the information may be not complete and correct. Could anyone help me to modify it?
Question: Suppose $X\sim N(0,1), \epsilon\sim N(0,1)$ ...
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If the $\varepsilon$ in $Y = \beta_0 + \beta_1 X + \varepsilon$ does not represent measurement error in $Y$, then what does it represent?
The classical simple linear regressoion model is
$$
Y = \beta_0 + \beta_1 X + \varepsilon. \tag{1}
$$
On page 3 of these slides, the author says if there are measurement errors in the outcome then we ...
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In reality, there is almost always measurement error in the independent variable(s), so why is this ignored in almost every linear regression model?
In the vast majority of cases, linear regression models are used in practice as opposed to the more complicated errors-in-variables models. For the sake of example, consider modelling height $Y$ vs ...
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Regression problem with "error in variables"
Suppose that there is a deterministic relation $y_t=ax_t$ where $x_t,y_t$ are real sequences or real functions and $a$ a constant.
But only $X_t=x_t+e_t$ and $Y_t+u_t$ can be observed, with $e_t, u_t$ ...
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How to do Error in Variables regression with known standard errors
I need some help with EiV regression and comparison of two methods.
I have used two different methods to estimate the size of the same population and would like to find out how good method 1 is ...
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Inverse Regression vs Reverse Regression
I'm aware there's a great number of questions which deal with the mathematical difference between the two, but I'm still confused as to best practice.
Basically I'm looking at a situation where we ...
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Big outlier in dependent variable
I have my data from the official statistics office of my country and I rechecked multiple times already. I have a big outlier skewing all my glm (poisson) modells to the extreme (like 5 times the ...
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What kind of statistical analysis is required to compare two methods for regression
I want to do comprehensive study of errors in variables and compare the results with regression for selected parameter estimation problems in my domain where it is expected to perform better in terms ...
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Errors-in-variables with correlated latent variable
Suppose I have data generated as follows:
$\tilde{X} = k \cdot X + u$, where X is an unobserved latent variable (say the temperature of the room) and X_tilda is the observed variable (say temperature ...
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meaning of error term being correlated with regressor
I have encountered the statement that "the error term and one of the regressors are correlated" a few times and I am having trouble understanding what is meant exactly. Let's say we have a DGP
$$y=\...
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Including model uncertainty in non-linear least squares minimization
The problem
I have experimental data $Y$ with heteroscedastic and normally distributed uncertainties characterized by covariance matrix $C_{exp}$. I want to fit the data using model $F(X, \beta)$ ...
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Difference between estimating parameters for prediction and estimating parameters for their own sake
In a 1989 paper on orthogonal regression, Ammann and Van Ness write:
An important caveat should be noted. The errors-variables-model is useful when the primary goal is to estimate the model ...
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Correct error estimation for linear fit
This may be a simple problem, but I want to be thorough in setting up my problem as I'd like to know why I should proceed in one of two ways (or another if someone thinks it is suitable), so please ...
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Exponential errors in variables model with known uncertainties
I have $N$ data points that I am trying to fit using a function of the form
$y_i = \prod_j {X_{i,j}}^{b_j}, \quad j=1..N$
where $\mathbf X$ and $\mathbf y$ are measured values. The form of this ...
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Why aren't "error in X" models more widely used?
When we calculate the standard error of a regression coefficient, we do not account for the randomness in the design matrix $X$. In OLS for instance, we calculate $\text{var}(\hat{\beta})$ as $\text{...
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How would you attempt to distinguish measurement error from a true distribution but no "true" singular value?
I am self-taught amateur in statistics and I have confusion is based calculations with error-in variables with the added object being measured having a no "true" value but a "true" range.
For me, ...
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If in this problem I regress $x$ on $y$ instead than $y$ on $x$, do I need to use an error-in-variables model?
I was trying to write an answer for this question:
Selection of data range changes coefficients too much in lmer (inverse regression)
Basically the OP has lots of data of Amplification vs Voltage (...
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Find error interval of linear relationship
I have two sensors of different quality capturing the same process, where one of them is much more accurate than the other. Hence, I want to find out how much better.
Let us for example say that the ...
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Fitting a logarithmic growth curve with error (an interval) of the explanatory variable?
I have a series of human growth data that I wish to fit to a 3 parameter logarithmic growth curve:
s(i) = Beta0 + B1*T + B2*ln(t), where s is a length and t is an age.
The only problem is that this ...
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Rotation changes correlation - correction from OLS
Let $X,Y$ be real random variables with finite variances, and with no loss of generality assume $\mathbf{E}[X] = \mathbf{E}[Y]=0$. For simplicity, I will focus on the case $\mathrm{Var}X \neq \mathrm{...
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Control Function Approach and Bootstrap
Let's start assuming that I have cross-sectional data on $y$, $x_1$, $x_2$ (see below for $y$, $x_1$, $x_2$).
I want to estimate the effect of variables $x_1$ and $x_2$ and their interaction ($x_3= ...
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What to do when expectation maximization results are invalid (they don't match the likert scale)
I have missing values (MCAR) for which I used EM to fill in those values. Some of the imputed values are negative integers or zero. I am using a likert scale to measure responses, and thus i need the ...
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small sample approach to simple linear regression with errors-in-variables (measurement errors)
I seek to estimate $b_1$ and $b_0$ from data of the form:
$$y_i = b_1x_i + b_0 + e_i, \quad i\in\{0,1,...,N-1\}$$
given $\{y_i\}$ and $\{\tilde{x}_i\}$ where $\tilde{x}_i=x_i + n_i$ (i.e., error-in-...
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correlation when x and y are uncertain
Suppose that for $1\le i \le N$
$$\begin{align}
Y_i^j &= f(X_i) + \epsilon_y \qquad &1 \le j \le R_y^i \\
Z_i^j &= af(X_i)+b + \epsilon_z \qquad &1 \le j \le R_z^i
\end{align}$$
where $...
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How do I use American Community Survey income estimates and standard errors in an error-in-variables model?
Income distributions tend to be highly skewed. Yet the American Community Survey (ACS) provides only two summary statistics for its median income estimates in small areas: the mean estimate and a ...
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How do errors in variables affect the R2?
I've got a question about errors in variables. So, if I run a standard linear regression to estimate b in y = a + bx, but my ...
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Dealing with independent variables where each point is an coefficient
I want to test if a behavior is influenced by population size. The former is measured as a continuous normal variable. The latter is estimated using Schnabel's method, and thus each sample has a ...
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OLS Assumptions - Errors are normally distributed
I am currently working on a research project based on the data of a big survey.
I derived a variable set, which I would like to investigate. Before starting with it, I would like to check the ...
