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).
63
questions
0
votes
0answers
15 views
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 ...
2
votes
0answers
47 views
meaning of error term being correlated with regressor [duplicate]
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=\...
4
votes
1answer
103 views
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)$ ...
0
votes
0answers
5 views
Mismatched sampling rates between predictors & response plus measurement errors on categories
Background
I'm unsure how to best model data from a widget manufacturing process with measurement "uncertainties" on categorical variables (relative to an ordered indexing variable) and an overall ...
1
vote
1answer
49 views
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 ...
0
votes
0answers
17 views
Estimating coefficients of a linear model with collinear dependent variables that have errors with known variances
I want to estimate the coefficients $\beta$ of the linear model
$Y=\beta X$
from observations of $(Y_i,X_i), i=1\ldots n$, where $X$ is multidimensional.
Two problems:
All variables have been ...
1
vote
1answer
60 views
Statistical library for orthogonal distance regression with a ridge penalty?
There are many libraries in R and python for doing orthogonal distance regression and for doing ridge regression separately. Is there one for doing them at the same time?
0
votes
0answers
15 views
Least squares regression when all variables have errors with known variances
I have a large number (n>1000) of independent measurements $x_i,y_i,z_i,\; i=1\ldots n$.
Each of these measurements has an error with a known variance $\sigma^2_{x_i}, \sigma^2_{y_i}, \sigma^2_{z_i}$...
0
votes
0answers
15 views
Is the maximum likelihood estimator unbiased for the error-in-variables model?
The following linear model for one scalar parameter $\theta$ is under consideration:
$$ \begin{cases}\pmb{\hat{x}} \theta = \pmb{\hat{y}} + \pmb{\epsilon}_y \ , \\
\pmb{x} = \pmb{\hat{x}} + \pmb{\...
1
vote
0answers
38 views
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 ...
2
votes
0answers
11 views
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 ...
0
votes
0answers
668 views
Non-negative least squares with errors-in-variables, no repeated measurements
In an experiment, I measured an enzymatic activity $y$ of many solutions containing mixes of different bacterial species. In each of these solutions, I also measured the number of individual cells of ...
4
votes
0answers
109 views
Prediction intervals with experimental errors
Engineer here, so apologies for my simplistic stats language.
I am missing some experimental data that I would like to "fill in" based on a linear regression to other data. I need to do this because ...
1
vote
0answers
17 views
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, ...
6
votes
1answer
242 views
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 (...
3
votes
2answers
200 views
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 ...
1
vote
0answers
32 views
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 ...
2
votes
0answers
68 views
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{...
8
votes
1answer
2k views
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= ...
0
votes
0answers
383 views
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 ...
3
votes
0answers
75 views
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-...
0
votes
1answer
30 views
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 $...
4
votes
1answer
876 views
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 ...
2
votes
0answers
20 views
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 ...
0
votes
1answer
100 views
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 ...
3
votes
0answers
60 views
Multiple errors-in-variables regression with collinearities
I have a $[k \times N]$ matrix of predictors / independent variables and a $[k \times N]$ matrix of predictands / dependent variables. I have uncertainty estimates for each predictor and each ...
3
votes
0answers
65 views
Intuition: Why do I have to worry about errors-in-variables?
I've read that (ordinary) linear regression assumes that there are measurement errors in the dependent variable, but no measurement error in the independent variables -- and if I have measurement ...
1
vote
0answers
136 views
Standard error of mean - under measurement error
I have two observations of a normally distributed random variable:
$$
X_1 = 0.02 \\
X_2 = 0.10
$$
Obviously the sample mean equals 0.06, and the standard error of the mean (SEM) is equal to 0.04.
...
2
votes
1answer
999 views
Bayesian errors-in-variables model definition in JAGS and symbolically
I'm fairly new to probability theory and am attempting to understand and implement an errors-in-variables simple linear regression model. I am assuming a model of the form
$$
Y=\theta X_a+\epsilon_Y ...
3
votes
0answers
717 views
Model selection: OLS vs TLS
I have two sets of real-valued data and I am interested in their correlation. From my perspective, there appear to be errors both variables, so I am inclined to perform a regression with TLS (Total ...
0
votes
1answer
159 views
Fit error-in-variables polynomial regression using mle2 (R)
I need to fit a polynomial regression that accounts for measurement errors. I found out how to do it with a mcmc model (using RJags) and I would like to do it with a Maximum Likelihood Estimator (...
3
votes
1answer
901 views
Total least squares with weights [duplicate]
I am looking for a way to perform weighted total least squares in R. I know one can use PCA for this as described nicely in the following post.
How to perform orthogonal regression (total least ...
0
votes
0answers
188 views
linear regression accounting for standard errors of variables
I am trying to figure out what is the best way to estimate beta why accounting for the uncertainty in x and y. For example, I have
...
2
votes
0answers
35 views
Signing the inconsistency of a control functions estimator with an incomplete set of instruments
I've got a model of the form
$$
y = 1\left(\alpha+\delta x+\beta_1\tilde v+\tilde\epsilon>0\right)
$$
$x$ is endogenous, and $\tilde v$ is a control function residual:
$$
\tilde v = x-Z'^{inc}\...
8
votes
4answers
1k views
Systematic/measurement error on a linear regression
Suppose I have a set of data ${(x_i,y_i)}$ in which the uncertainty in the measurements ${(\Delta x_i,\Delta y_i)}$ (which come from the propagation of systematic errors from the measurement apparatus)...
5
votes
0answers
139 views
Total least square intuition
I have yet to find a good intuitive explanation of TLS. Online resources tend to focus on the vertical vs. perpendicular square error pictures (I don't need to see perpendicular lines to understand ...
2
votes
0answers
550 views
Errors-in-variables multivariate polynomial regression (R)
(EDIT: the question has been modified just a little bit to be more specific)
I want to fit a multivariate polynomial regression that accounts for measurement errors (an Error-in-Variables model).
...
13
votes
1answer
861 views
Biased estimator for regression achieving better results than unbiased one in Error In Variables Model
I am working on some syntatic data for Error In Variable model for some research. Currently I have a single independent variable, and I am assuming I know the variance for the true value of the ...
1
vote
0answers
222 views
Deming Regression/Errors-in-Variables with replicates
I have a question about a model related to Deming regression and would appreciate some help and/or publications to further study this model.
Statistical Model:
\begin{align}
X_{i,j}&=\mu_{X,i}+\...
2
votes
0answers
163 views
Estimating variances in orthogonal regression
In orthogonal regression it is assumed that both variables have noise. I'm interested in the simplest possible case. That is, I have a very large number of data points $(X_1,Y_1), ..., (X_n,Y_n)$. ...
4
votes
0answers
416 views
Errors-in-Variables model for logistic regression
Simple question: I am familiar (though don't have tons of experience) with errors-in-variables regression. From what I have seen, this mostly is used with continuous outcomes in a linear model.
A) Is ...
5
votes
1answer
764 views
Intuitive meaning of error-in-variables
I understand the explanation of the example of error-in-variables used wikipedia. What I do not understand is how could we explain intuitively the error-in-variables problem? One way would be to say ...
2
votes
0answers
60 views
Linear regression with estimates of error in predictor
I have data with two different kinds of measurements at the same set of $S$ sites. One of these (call it $X$) returns m estimates at each site, which are not necessarily independent of one another. So ...
2
votes
1answer
724 views
How to estimate mean and standard deviation of a normal distribution from noisy data?
I have $n$ observations, $x_i$ following a normal distribution. I would like to estimate $\mu$ and $\sigma$ from my samples. Normally I would simply
estimate
$\mu=(\sum x_i)/n$ and
$\sigma^2=\sum (...
3
votes
1answer
102 views
Selecting variables using SAS and R - all effects are significant even when shuffling the data
Dear all: I need to test which effects I should include in my model for genetic evaluation of cows. I was using the following code in R:
...
1
vote
0answers
25 views
Using aggregated data from a database with data from another
Let's say I have two databases, in the first (DB1) there is individual data on how much people trust in the government ($X_{j,r}$), and on the second (DB2) there is individual data on how much people ...
1
vote
1answer
795 views
Probability limit calculation
My class notes list the following steps for calculating a plim under classic errors in variables:
$$
{\rm plim}\ \beta_1 = \frac{{\rm cov}(\beta_0 + \beta_1 x_1 + \epsilon - \beta_1 e, x_1)}{{\rm var}(...
0
votes
1answer
1k views
Probability limit formula for coefficient in errors in variables regression
I found an online resource which lists the plim formula for a simple regression under the classic errors-in-variables assumption as:
$$
\text{plim }\beta_1=\frac{{\rm Cov}(y, x_1)}{{\rm Var}(x_1)}
$$
...
7
votes
1answer
353 views
Comparing power law fits with large uncertainties
I want to test how well my data fit the particular power law:
$y=ax^b$
where $b$ , for physical reasons, should equal exactly $-0.5$. I would like to find the probability that the data do not obey ...
3
votes
1answer
492 views
How to do regression with error in variables and known correlations among the errors?
After the very satisfying answer to:
How to do regression with known correlations among the errors?
I take the question to my next point of interest:
What can you do when you have a regression with ...
