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).

40 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
6
votes
0answers
77 views

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 ...
5
votes
0answers
85 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 ...
5
votes
0answers
160 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 ...
4
votes
0answers
135 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 ...
4
votes
0answers
533 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 ...
4
votes
0answers
299 views

Regression model with heteroskedasticity in both variables

I've been learning (lurking) from this site for a while and I finally have a question I haven't seen answered yet. I'm doing a flight test and trying to fit the resulting data to linear line. From a ...
3
votes
2answers
305 views

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 ...
3
votes
0answers
83 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-...
3
votes
0answers
76 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
988 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 ...
3
votes
0answers
112 views

Confusion related to calculation of likelihood

I was reading this paper related to Learning from multiple annotator using Gaussian processes. The idea is if we don't have the actual ground truth of a certain data, but only the labels from some ...
2
votes
0answers
35 views

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 $e_t, u_t$ ...
2
votes
0answers
15 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 ...
2
votes
0answers
95 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{...
2
votes
0answers
55 views

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 ...
2
votes
0answers
21 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 ...
2
votes
0answers
36 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}\...
2
votes
0answers
610 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). ...
2
votes
0answers
204 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 $(X_1,Y_1), ..., (X_n,Y_n)$. ...
2
votes
0answers
62 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
0answers
567 views

Statistical Tests with Data Having Measurement Errors

For example, can the results of the t test on y1 and y2 be interpreted in the usual way (i.e., like the results of the t test on x1 and x2)? If not, how should I go about testing whether or not y1 and ...
1
vote
0answers
50 views

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 ...
1
vote
0answers
82 views

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 ...
1
vote
1answer
61 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 ...
1
vote
1answer
185 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?
1
vote
0answers
56 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 ...
1
vote
0answers
18 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, ...
1
vote
0answers
35 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 ...
1
vote
0answers
142 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. ...
1
vote
0answers
272 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}+\...
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
1k 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}(...
1
vote
1answer
746 views

Uncertainty from linear fit on additional data

Let's say I have 5 known data points with coordinates $X$ : Area under curve $Y$ : Activity The 5 points have individual error ($\Delta X_{i}$,$\Delta Y_{i}$) on both $X$ and $Y$ and I know that ...
0
votes
0answers
25 views

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 $X\sim N(0,1), \epsilon\sim N(0,1)$ ...
0
votes
0answers
8 views

Interpolating between poorly-defined stratification levels - modeling with very large errors-in-variables

I'm trying to estimate the mean response error associated with a measurement device (Device A) for concentration of a chemical in solution. The measurement device uses a disposable component whose ...
0
votes
0answers
18 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 ...
0
votes
0answers
453 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 ...
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 $...
0
votes
1answer
245 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 (...
0
votes
0answers
203 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 ...