# Tag Info

1 vote

### How does expectation maximization relate to weighted least squares?

While applying EM on a mixture of Gaussian (like your case), part of the steps do coincide with weighted least squares. E step: Taking expectation w.r.t. $C$ on the loglikelihood results in a "...
Accepted

### Does the matrix notation for OLS loss function assume that indexing a row from $X$ return a column or row vecotr?

Capital $X$ is the matrix of all feature values for all subjects, while lowercase $x$ is the vector of feature values for one subject. The lowercase $x$ is used in this notation to indicate that it is ...

### Interpretation coefficients categorical variables

It appears that you have several binary explanatory variables, all of which are binary and enter the model either as simple main effects or a 2-way interaction. For the coefficient of a main effect, ...

### How can I quantify uncertainty for a least squares estimator in a multivariate linear regression with covariance structure?

A general result from least squares estimation is that $$\boldsymbol{\hat{\beta}}=(X'X)^{-1}X'\mathbf{y},$$ where we can treat $\mathbf{C}=(X'X)^{-1}X'$ as constant. Then, we can apply the variance ...

### ML vs WLSMV: which is better for categorical data and why?

Your question does not specifically reference factor analysis (FA) or structural equation modeling (SEM), though I will assume you are broadly interested in differences between estimators for ...

### When does adding a new predictor not increase $R^2$ in OLS?

This diagram from the answer at https://stats.stackexchange.com/a/113207/919 abstractly (but accurately) depicts the space $X_1$ spanned by all the (current) explanatory variables, the response ...
1 vote
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### How to prove OLS estimator still unbiased if omitted variable(s) are independent of included variables

This is just a question of whether $X_1^\top X_2=0.$ I.e. is every column of $X_1$ orthogonal to every column of $X_2$? In particular, if an $y$-intercept term is included in the regression involving ...
1 vote
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### How to model a standardized index in a regression?

With one caveat, there's no problem doing anything you would do with a regular variable to an index. After all, some 'regular' variables are indexes to start with. So as @patrick-coulombe notes, it'll ...

### What is the objective function for weighted lasso & ridge?

It's not applied to the regulariser term. Consider eg a repeated data set.. you can rewrite it with weights for the count of each data point (X,y) ie distinct row. The weights would be on the error ...

### Homoskedasticity and Collinearity

There really isn't anything saying that these two things are explicitly related. You can have two predictors that are: Almost perfectly collinear with heterogenous variance Almost perfectly collinear ...
1 vote
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### Why aren't OLS standard errors becoming smaller in the presence of serial correlation?

I figured out the problem. As Baltagi (2008) states in eq. 5.34 (p. 111), the estimated variance of the point estimate when serial correlation exists is the original estimator (i.e., s^2(X'X)^{-1}) ...

### Fixed Effects causes Multicollinearity

Multicollinearity means that the contribution of a variable (or a combination of variables) cannot be identified because it could be emulated by another variable (or a combination of them). Looking at ...

### biased estimation of variable correlated with endogenous variable

Maybe I misunderstand the setup, but I do not directly see this spillover bias: By linear projection theory, least squares on the equation for $Y$ will, for $D=(Z\; X)$ and $\hat\beta$ the vector of ...
1 vote

### Definition of fixed effects used in Journal Papers

This is an economics-flavored answer, which is appropriate given your research question. Other fields have their own jargon that is fairly different. There are typically two ways to estimate fixed ...

### Why not use instrumental variable directly as a covariate in the regression?

Well actually you could. Now suppose you have two groups of IVs, $Z_1$ and $Z_2$, both could be vectors. Suppose you include $Z_1$ in your regression with $Y$, then they're called "included ...