# Tag Info

50

Let me share a contrasting view point. I'm an economist. I was trained in econometrics using SAS. I work in financial services and just tonight I updated R based models which we will use tomorrow to put millions of dollars at risk. Your professor is just plain wrong. But the mistake he's making is VERY common and is worth discussing. What your professor ...

34

There are some terminology differences where the same thing is called different names in different disciplines: Longitudinal data in biostatistics are repeated observations of the same individuals = panel data in econometrics. The model for a binary dependent variable in which the probability of 1 is modeled as $1/(1+\exp[-x'\beta])$ is called a logit ...

24

It is not more or less reliable than other software. Base and recommended R is probably less prone to errors than contributed packages might be, but it depends on the authors. But R's biggest advantage is that you can check yourself whether it is! It is free software, not like Stata or SPSS or similar. Hence even if it was unreliable, it would be detected ...

23

The $t$-values and $R^2$ are used to judge very different things. The $t$-values are used to judge the accurary of your estimate of the $\beta_i$'s, but $R^2$ measures the amount of variation in your response variable explained by your covariates. Suppose you are estimating a regression model with $n$ observations, $$Y_i = \beta_0 + \beta_1X_{1i} + ...+ ... 15 There are IMHO no formal differences that distinguish machine learning and statistics at the fundamental level of fitting models to data. There may be cultural differences in the choice of models, the objectives of fitting models to data, and to some extend the interpretations. In the typical examples I can think of we always have a collection of models ... 15 Your professor makes some bold claims. I suspect that the problem was unfamiliarity with R language, not the actual results produced. I work in a company which does a lot of econometric modeling and we do everything in R. I also converted my economist colleague into using R. Concerning field of economics in my personal experience, reliability issue might ... 14 I am an economist and I have been working in research for 4 years now, mostly doing applied econometrics. There are plenty of econometrics packages out there, and there is room for all of them. In my view, in economics, Stata is used for almost everything but time series, Rats, Eviews and Ox are used for time series, Matlab and Gauss are used for more low ... 13 In the context of linear regression in the social sciences, Gelman and Hill write[1]: We prefer natural logs (that is, logarithms base e) because, as described above, coefficients on the natural-log scale are directly interpretable as approximate proportional differences: with a coefficient of 0.06, a difference of 1 in x corresponds to an ... 12 It is best to explain in terms of linear regression, since it is the main tool of econometrics. In linear regression we have a model:$$Y=X\beta+\varepsilon$$The main difference between other statistical fields and econometrics is that X is treated as fixed in other fields and is treated as random variable in econometrics. The extra care you have to use ... 10 "Practical" and "simple" suggest least squares regression. It's easy to set up, easy to do with lots of software (R, Excel, Mathematica, any statistics package), easy to interpret, and can be extended in many ways depending on how accurate you want to be and how hard you're willing to work. This approach is essentially your "weighting scheme" (2), but it ... 10 There is no very strong reason for preferring natural logarithms. Suppose we are estimating the model: ln Y = a + b ln X The relation between natural (ln) and base 10 (log) logarithms is ln X = 2.303 log X (source). Hence the model is equivalent to: 2.303 log Y = a + 2.303b log X or, putting a / 2.303 = a*: log Y = a* + b log X Either form of the ... 9 As a medical statistician with no previous knowledge of econom(etr)ics, I struggled to get to grips with instrumental variables as I often struggled to follow their examples and didn't understand their rather different terminology (e.g. 'endogeneity', 'reduced form', 'structural equation', 'omitted variables'). Here's a few references I found useful (the ... 9 I think you're right. Let's distill your argument to its essence: \widehat \theta_N minimizes the function Q defined as Q(\theta) = {1 \over N}\sum_{i=1}^N q(w_i,\theta). Let H be the Hessian of Q, whence H(\theta) = \frac{\partial^2 Q}{\partial \theta_i \partial \theta_j} by definition and this in turn, by linearity of differentiation, equals ... 9 I'd be very careful of anyone who claims a fact but never backs it up with anything substantial. You can easily turn his arguments around. For example, people getting paid to write code could have LESS incentive to get it right because there is an expectation that their code will be correct, whereas the typical basement dweller wants to make a commit that ... 9 No, it doesn't mean that they are unrelated. R^2 only measures linear relationships. For example, if X is symmetric around zero and Y = X^2 + \epsilon, where \epsilon is some error independent of X, then the R^2 for the regression of Y on X will be zero--even if \epsilon \equiv 0, so that there is a perfect deterministic relationship ... 8 Becasue Var(u|x)=E(u^2|x)-E^2(u|x)=E(u^2|x)-0^2=E(u^2|x)=E(u^2)=\sigma^2, since u has a zero conditional expectation. Here I used the fact that u is independent of x. Therefore, (roughly speaking) each function of u is independent of x as well. So in particular u^2 is independent of x. This means that E(u^2|x)=E(u^2). 8 There is a simulated data set called outliers in the TeachingDemos package for R. If you remove the "outliers" using a common rule of thumb, then relook at the data and remove the points that are now outliers and continue until you have no "outliers" you end up trowing away 75% of the data as "outliers". Are they really unusual if they are the majority of ... 7 My view is that the models used in economics and the other social sciences are useful only insofar as they have predictive power in the real world - a model which doesn't predict the real world is just some clever math. A favorite saying of mine to colleagues is that "data is king". It seems to me that your question raises two critiques of a predictive ... 7 There is a (fairly limited) set of statistical tools for so-called "causal inference". These are designed for actually assessing causal relationships and are proven to do this correctly. Excellent, but not for the meek of heart (or brain, for that matter). Apart from that, in many instances, the ability to imply causality is much more a consequence of your ... 7 Model estimation is the process of picking the best (according to some metric) kind and structure of model. Estimation may include calibration. Calibration is the process of finding the coefficients that enable a model (the kind and structure of which is already determined) to most closely (according to some metric) reflect a particular known dataset. So: ... 7 Typically lognormal distributions or sometimes pareto distributions are used to model the distribution of income. Here you can find information how well these distrubtions fit real data for Germany, UK and the US: http://ideas.repec.org/p/wpa/wuwpmi/0505006.html Here is a proposal to use a generalized lognormal distribution ... 7 You can easily convince yourself that this works with a simulation, though this is not really a substitute for a proof. D-in-D is really the just the difference between 4 means, so any model that estimates the expected value can be turned into a D-in-D estimator by using a dummy for belonging to the treatment group, a dummy for the after-treatment periods, ... 7 To manually verify the predictions derived from using polr() from package MASS, assume a situation with a categorical dependent variable Y with ordered categories 1, \ldots, g, \ldots, k and predictors X_{1}, \ldots, X_{j}, \ldots, X_{p}. polr() assumes the proportional odds model$$ \text{logit}(p(Y \leqslant g)) = \ln \frac{p(Y \leqslant g)}{p(Y ...

7

There appears to be some discrepancy here regarding what a proof of identification entails and what you are trying to prove. Let me rewrite your model as $$Y_i = \exp(\boldsymbol{X}_i'\boldsymbol{\beta}^0) + U_i$$ where $\boldsymbol{X}_i = [X_{1i},\ldots, X_{Ki}]'$, together with the assumption that $\mathbb{E}(U_i \mid \boldsymbol{X}_i)=0$. It appears ...

7

Often the relationship between y and x is nonlinear. There are a variety of solutions. One solution is to add polynomial terms and the first one to look at is usually $x^2$. But you should first look at a scatterplot of x and y; you should also look at the residuals from the linear model without the quadratic term. But it turns out that many relationships ...

6

In addition to the links that were given in comments, here are some further pointers: Association rules and frequent itemsets Survey on Frequent Pattern Mining -- look around Table 1, p. 4 About Python, I guess now you have an idea of what you should be looking for, but the Orange data mining package features a package on Association rules and Itemsets ...

6

The quotation in full can be found here. The estimate $\hat{\theta}_N$ is the solution of minimization problem (page 344): \begin{align} \min_{\theta\in \Theta}N^{-1}\sum_{i=1}^Nq(w_i,\theta) \end{align} If the solution $\hat{\theta}_N$ is interior point of $\Theta$, objective function is twice differentiable and gradient of the objective function is zero, ...

6

In the usual case with a log variable, the model is \begin{align} \log(y) &= a + b\log(x) + \varepsilon\newline \text{or}\quad y &= e^a x^b e^\varepsilon, \end{align} where $\varepsilon\sim\text{N}(0,\sigma^2)$ and $b$ is the elasticity. In the situation you mention, \begin{align} y &= \exp[a + b\log(x)] + \varepsilon \newline \text{or}\quad y ...

6

The original White paper where the test statistic was proposed is an enlightening read. This excerpt I think is of interest here: ...the null hypothesis maintains not only that the errors are homoskedastic, but also that they are independent of the regressors, and that the model is correctly specified... Failure of any of these conditions cal ...

6

You answer your own question. There is nothing different than backing out function of $x$ from the conditional expectation conditioned on $x$. Introduce definition $$g(x)=E(y|x)$$ Then $$Eyg(x)=E[E[yg(x)|x]]=E[g(x)E[y|x]]=E[(E[y|x])^2]$$ And we get your result. However your last statement is false. $E(y|X)$ is a random variable which is different from ...

Only top voted, non community-wiki answers of a minimum length are eligible