20
votes
Accepted
Difference between one-way and two-way fixed effects, and their estimation
The unobserved effects model is modeled as:
\begin{equation}
y = X\beta + u
\end{equation}
where
\begin{equation}
u = c_{i} + \lambda_{t} + v_{it}
\end{equation}
A one-way error model assumes $\...
7
votes
meta-analysis: expected Q and observed Q
Assume the "summary effect size" is the inverse variance weighted mean
$$M = \frac{1}{\sum_{i=1}^k (1/V_i)}\sum_{i=1}^k \frac{Y_i}{V_i} = \sum_{i=1}^k \omega_i Y_i$$
(thereby defining the ...
- 334k
6
votes
meta-analysis: expected Q and observed Q
Here's a quick and simple explanation.
Q is chi-square distributed. The expected value of chi-square under the null hypothesis is the degrees of freedom.
- 19k
5
votes
Accepted
Computation of Network Homophily / Heterogeneity
The second one (igraph function) is correct. The first one does not take into account the baseline probability that two people from the same group will be connected by random change.
Because your ...
- 392
5
votes
Two Study Meta-Analysis: Fixed- vs. Random-effects and heterogeneity
To answer your questions more or less in order.
The value of $\tau^2$ is estimated as zero so under those circumstances the two models will give the same result. It is not because you have two studies....
- 18.4k
5
votes
Accepted
How can I account for heterogeneity at the author level in a meta-analysis?
I would recommend fitting a model with random effects for authors and studies within authors. This is the 'three-level' model described by Konstantopoulos (2011). An example illustrating such an ...
- 17.9k
5
votes
Accepted
Causal inference where potential outcome is somehow "violated"?
I agree that there is some confusion about the "unit" of analysis here. It's neither the ad nor the viewer, though; it's the instance of showing an ad to a viewer. And there is only one ...
- 36.8k
4
votes
Accepted
Clarification of LLNs when non i.i.d. observations
Although the comments are of course right that iid-ness is the leading case, and that dependence is the leading departure from iid-ness, it is not necessary for a LLN that the means are identical.
...
- 34.8k
4
votes
Is it worth doing (single-armed) meta analysis if the studies' heterogeneity is very large?
At the risk of stating the obvious the first thing is to establish what form the heterogeneity takes and whether there is any obvious explanation for it. If the studies are single arm studies they ...
- 18.4k
4
votes
Accepted
Is it worth doing (single-armed) meta analysis if the studies' heterogeneity is very large?
Single arm studies always involve a comparison to what would have happened without the intervention. If that comparison is done sensibly, then putting the results of these comparisons into a meta ...
- 35.2k
4
votes
Causal inference where potential outcome is somehow "violated"?
You misunderstood the definition of unit there. One unit, individual, can not be in the control group and the treatment group at the same time. You can only observe the effect of ONE intervention on ...
- 1,063
4
votes
Causal inference where potential outcome is somehow "violated"?
I would set up your data as an ad-level crosssection, where:
Each row is a distinct ad
Ad characteristics are the other columns.
The outcome column is the treatment-control difference in the two ...
- 38.3k
3
votes
Accepted
Re: Random Effect Model in Binomial Proportions Meta-analysis
When you have estimated the within study variance ($v_i$) using whatever method is appropriate then in a fixed effects analysis the weights are just its reciprocal $w_i = \frac{1}{v_i}$
However in ...
- 18.4k
3
votes
Accepted
Conducting a subgroup analysis with regression modeling
Your reasoning is correct - as already commented by @user158565, a single model is generally better, as you are able to obtain a proper CI for the heterogeneity term.
Another major difference is ...
- 2,270
3
votes
Accepted
I-Squared: From Calculation to Concept
Though $I^2$ is commonly reported as an absolute measure of heterogeneity, as you describe, Borenstein et al. (2017) caution against this. It is a proportion (i.e., relative), and only in strict ...
- 5,566
3
votes
proportional meta-analysis, small confidence intervals and I square of 100 %?
What you are seeing is entirely consistent. If you have very narrow confidence intervals you will see very high values for $I^2$. In a paper entitles "Undue reliance on $I^2$ in assessing ...
- 18.4k
3
votes
Meta analysis: is there such a thing as too little heterogeneity?
From what I can see, you are meta-analyzing correlation coefficients using Fisher's z-transformation, which is appropriate. I'm assuming that the input data are entered correctly, and the analysis ...
- 720
3
votes
Accepted
Meta-analysis: significant heterogeneity vs. significant between-study variance
Let $\theta_{ij}$ denote the true effect for outcome $j$ in study $i$. The test for heterogeneity given in the output tests the null hypothesis $H_0: \theta_{ij} = \theta$ across all outcomes and ...
- 17.9k
3
votes
How can I account for heterogeneity at the author level in a meta-analysis?
A couple of options including meta-regression that we present in this paper: Can authorship bias be detected in meta-analysis? by Abou-Setta AM et al. (2019).
One thing you will need to note is that ...
- 1,290
3
votes
Accepted
OLS when $\beta_i$ varies across observations
For the model as you have written it (no intercept) the Wikipedia page provides the formula for the slope estimate $\hat\beta$:
$$\widehat{\beta} = \frac{ \sum_{i=1}^n x_i y_i }{ \sum_{i=1}^n x_i^2 } =...
- 102k
3
votes
How to interpret Cox Model with time-varying coefficients
There are quite a few reasons why proportionality does not hold. One of them is omission of an important variable and thus you get a wrong model that may appear as time-varying coefficients. Let's ...
- 550
3
votes
Accepted
Causal inference for multiple treatments with an observed set of properties
How the problem is described (i.e., $T$ is the area assigned and $Z$ is the characteristics of that area), it sounds like the features of $Z$ are already implied by $T$. For a discussion of how ...
- 2,617
3
votes
Accepted
Clustering on n features while maximizing the heterogeneity on m remaining features
I will offer a simple example for numerical data. The idea behind it can be extended to the case of categorical data without major conceptual difficulty (as far as I can see).
Suppose you have two ...
- 69.5k
3
votes
Conditional Average Treatment Effects
Firstly, we can express this via potential outcomes. Building off the provided notation, we can index the variables by time. So $X_0$ and $W_0$ would be treatment and the covariates measured as ...
- 2,617
2
votes
Heterogeneous treatment effects with 2SLS local average treatment effect (LATE)
This is maybe a late answer (I happened upon it while searching for a question of my own), but the answer to your question is that your 2SLS should include SES as a control variable in the first and ...
- 5,047
2
votes
Accepted
Intuition on simple linear regression signal plus noise model
Check the related question asking about logistic regression. The quotes you posted sound confusing, but what they are saying is that $Y_1,Y_2,\dots,Y_n$ are independent, but not identically ...
- 141k
2
votes
Accepted
Panel regression with multiple fixed effects and heterogeneity
I agree with you that the most natural model to estimate is the two way fixed effects model
$$
Y_{it} = X_{it}'\beta + c_i + \theta_t + v_{it}
$$
where $c_i$ is an individual fixed effect and $\...
- 606
2
votes
Calculating Standard Error of Tau - Meta Analysis
The problem with what you suggest is that the confidence interval for $\tau$ or, for that matter, $\tau^2$ is not symmetric about the central value so the standard error is not really useful for ...
- 18.4k
2
votes
Accepted
How to interpret heterogeneity in a meta analytic model
This result means that there is no more variance than you would expect by chance between the studies, and you do not have evidence for heterogeneity. This does not mean that there is no heterogeneity, ...
- 19k
2
votes
I-Squared: From Calculation to Concept
To add to @jsakaluk's answer specifically about your second point and your bonus.
It is possible and helpful to give a confidence interval for $I^2$. See this article by Ioannidis and colleagues "...
- 18.4k
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