38
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Accepted
Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
Yes
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers ...
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27
votes
Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
Following on existing answers, I wanted to give a concrete example. Imagine trying to figure out if the gas pedal affects the speed of a car. You observe how far the gas pedal is pressed and how fast ...
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13
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Difference Omitted Variable Bias and Confounding?
Omitted variable bias (OVB) is agnostic to the causal relationship between $X$ and $Z$. It concerns only the ability to estimate $\tau$ in the structural model for $Y$. The joint distribution of $Y$, $...
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7
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Using a DAG to understand omitted variable bias in OLS vs Binary Dependent Variable Regression
You are confusing confounding and noncollapsibility. In logistic and probit models, the difference between the focal coefficient in a covariate-adjusted vs. unadjusted model is not due just to ...
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7
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Omitted variable bias vs. Multicollinearity
Usually, you would not care about both of them simultaneously. Depending on the goal of your analysis (say, description vs. prediction vs. causal inference), you would care about at most one of them.
...
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6
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Can a confounding factor hide a possible causal relationship? (as opposed to find a spurious one)
First, I think you are mixing the usage of "correlation" and "causal relationship". They are different things. To discuss the differences, and how to find "causal relationship", we need a lot of ...
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5
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How is the omitted variable bias formula derived?
Here's an example of how one analyzes such a situation. Suppose that the model
$$E[Y\mid X_1,X_2] = \beta_1 X_1 + \beta_2 X_2$$
holds where $X_1,$ $X_2,$ and $Y$ are random $n$-vectors. If you omit ...
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5
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Omitted variable bias in ordered logistic regression query
Yes, the same holds true.
Note that omitted variable bias is an epistemic, not a technical problem. It means you lack a meaningful interpretation of results from a statistical model, e.g. ...
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4
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Omitted Variable Bias (OVB) and multicollinearity
This is a good question. The confusion stems from the "assumption" of no multicollinearity. From the Wikipedia page on multicollinearity:
Note that in statements of the assumptions ...
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What would it take for the omitted-variable bias from multiple omitted variables to cancel out?
Expanding on the comment as an answer. First write the true model as
$$ Y_i = X_{1i}^T\beta_1 + X_{2i}^T\beta_2 + \epsilon_i \tag{1}$$
where $X_{1i}$ is a $K_1 \times 1$ vector of covariates (resp. ...
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3
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Adjusting for confounding in linear regression model
The "omitted variable bias formula" as stated in Stock and Watson, Introduction to Econometrics (also available at https://www.econometrics-with-r.org/6-1-omitted-variable-bias.html) says ...
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2
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Does confounding always imply endogeneity?
I would say no. Confounding per se could be endogenous, or it might not be. But if the confounding variable is measured, then it's no longer endogeneity. Here's an example of endogenous confounding:
...
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2
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Omitted variable bias vs. Multicollinearity
If your goal is inference, multicollinearity is problematic. Consider multiple linear regression where the beta parameters help us estimate the increase or decrease in Y for a unit increase in X1, all ...
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My instrument (z) only affects y through x, but y affects z directly. Is my instrument valid?
If it is the case that $Y$ affects $Z,$ then $Z$ cannot be an instrument. By definition, an instrumental variable has to be $d$-separated from $Y$ in $G_{\alpha}$ and $d$-connected to $X.$ Your ...
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Difference between the concept of omitted variable bias in econ and epidemiology/social sciences (Elwert and Winship)
Omitted variable bias is very specific and refers to the bias in the parameter $\beta$ when omitting the variables $Z$ from a regression model of the following form:
$$Y = \alpha + X\beta + Z\gamma + \...
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2
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Accepted
Omitted variable problem
Start with
$$y=\beta_0 +\beta_1 x_1 + ... + \beta_k x_k + \gamma q +\epsilon.$$
Say that the mean value of $q$ is $\bar q$. Then centering $q$ around its mean gives $q_c=q-\bar q$. Substitute into the ...
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What would it take for the omitted-variable bias from multiple omitted variables to cancel out?
One could assume (essentially a special case of Yashaswi's +1 answer) a structural model like
$$
y=\beta_0+\beta_1x+\beta_2w_1+\beta_3w_2+u,
$$
where $Cov((x,w_1,w_2)'u)=0$ and interest is on $\beta_1$...
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1
vote
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Omitted variables problem
Section 4.1 of the Wooldridge text describes what's being considered:
The correlation of explanatory variables with unobservables is often due to self-selection: if agents choose the value of [...
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1
vote
Adjusting for confounding in linear regression model
It depends on the substantive nature of the relationship between the confounder and the other variables. Here's one example
Let's say that you are running a model trying to predict income as a ...
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vote
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Endogeneity coming from omitted variable vs measurement error
I don't know if I'm the best to explain this but I'll give it a go. A measurement error is, for instance, when the person was supposed to code you as LFG in a dataset, but coded you as GFL. So then ...
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Should I adjust for a confounder when it is colinear with a predictor?
that's not a bug that's a feature, you just showed that when you control for x2, x1 has no effect on y, which is exactly what you wanted to know. Good job.
You also learned that x1 is highly ...
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Trade-off between omitting variables or dropping observations in multivariate logistic regression
This is an unnecessary trade-off, as data don't have to be "missing completely at random" (MCAR) to include cases with missing values in the analysis. In practice, you often have data "...
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1
vote
Accepted
Is omitted variable bias possible with a perfectly correlated dependent and independent variable?
Yes, because omitted variable bias depends on the underlying causal question you want to ask.
Suppose you are interested in explaining the causal effect of schooling on earnings (just to give an ...
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