6

I would suggest the following approach: Write down all the variables you have and draw a DAG (causal diagram) which shows the proposed inter-relationships between all the variables. This should be informed by expert knowledge of the subject domain. You should potentially include confounders and competing exposures, and exclude mediators. Be careful of over-...


5

You'll notice that in in Hernan et al. (2009), that is not the formula they use for the weights. The formula you provide is the unstabilized weight formula, and the formula used in the paper is the stabilized weight formula, $$ sw_i=\prod_{t=1}^{T}\frac{P(A_t=A_{i,t}|\overline{A}_{t-1}=\overline{A}_{i,t-1})}{P(A_t=A_{i,t}|\overline{A}_{t-1}=\overline{A}_{i,t-...


4

Stationarity is a bit of a distraction because this is a simple property of any two random variables $Y(t)$ and $Y(t-u)$ having common (finite) variances $\sigma^2$ and zero expectations. Fix $t$ and $u.$ Because $E[Y(t)]=E[Y(t-u)]=0$ and $E\left[Y^2(t)\right] = E\left[Y^2(t-u)\right] = \sigma^2,$ $$\operatorname{Cov}(Y(t), Y(t-u)) = E[Y(t)Y(t-u)] = \sigma^2 ...


4

To add to the context here, finding significant predictors is easy. If you want a p < .05, then all you need is 100 or so predictors and you'll get a handful that come out as significant. Significance of predictors is hardly interesting unless there's good theoretical reason to believe that statistical significance corresponds to clinical interest. You ...


4

Unlike maximum likelihood estimation for a well-chosen correlation structure, the cluster bootstrap doesn't really "know" about the correlation structure. The cluster bootstrap allows for a fairly general correlation structure (just as the robust cluster sandwich estimator does) but that's not necessarily enough to be optimal. The sandwich ...


4

The ancova model will be biased if the study was not randomized, and the change score approach does not properly measure causal effects in observational studies. So the mixed model might be the best approach. The question boils down to: Does gender NA at t1 are ok in the model? Or should the t0 values be inputted also at t1? Is the 0 variance between t0 and ...


3

This is a big question with no right answer. A lot depends on your audience and field. The fact that you are citing Baltagi suggests you might be in the econ area. If so, you are going to have a hard time convincing colleagues/readers that random effects are appropriate unless you want to do something that absolutely cannot be done in a fixed effects model. ...


3

From the estimation perspective, pweights is internally used the same way as any other weight. in OLS: $$ min_{\beta} = \sum{(y-\beta X)^2 * w} $$ The only difference with other methods is during the estimation of standard errors. When you use pweights, is like requesting robust standard errors. (sandwich formula). For further details on how exactly weights ...


3

Basically it is because of difference in treatment timing. There is no single time $t^\star$ such that for any group who is at some time treated, it will be treated at any time after $t^\star$. When there is no single time of treatment initiation it is impossible to define a single post treatment variable. In the staggered design several groups are treated ...


3

As can be deduced from reviewing some of the 4 digit SIC codes, the first 3 digits of the 4 digit code indicate the group. Here are some examples: Code 5812: Eating Places belongs to "Industry Group 581: Eating And Drinking Places" Code 7999: Amusement and Recreation Services, Not Elsewhere Classified belongs to "Industry Group 799: ...


3

Plotting the aggregate trends across groups is one way to proceed, but when the adoption years vary so widely across $i$ then this approach is a bit messy. Assessing coefficient leads in one approach. Consistent with a Granger-type causality test, leading values of the policy variable should not predict the current outcome. Here is one specification: $$ y_{...


3

The default random effects estimator, Swamy-Arora, makes use of the between model to estimate the variance components, meaning it needs to estimate the between model (and the within model). Have a look what happens when you try to estimate the between model directly: covariates are dropped until the model becomes estimable (note the information in the ...


3

The fixed effects model your estimating is akin to estimating a separate intercept for each sireID. The unit-specific intercepts don't appear in your summary output, but you can ask for them with the following function: fixef(fixed). Estimating fixed effects along the other dimension (e.g., effect = "twoways) isn't going to return a global intercept. ...


3

Assuming that each subject is only in one group, you have a nested design. Conceptually, it makes more sense to treat group as a fixed effect. As you have only three groups, it wouldn't make much sense statistically speaking anyways because you'd be asking the software to estimate a variance for group assuming a normal distribution from only three ...


2

I'm not sure this is a mediation model as much as it's a growth curve model with a slight twist. You want to know if prior week's rumination level is associated with subsequent week's depression. Is that right? If so, then just create a "lagged" version of ruminate such that a row of data associated with week 2 has a version of ruminate that is its ...


2

In settings with more than two cities, we can still compute the difference-in-differences coefficient. I will show you how it works using a very simply illustration in R, though I highly recommend @DimitriyV.Masterov's answer linked in the comments. Stata's margins command is very robust, though the margins package in R is able to replicate Stata's output. ...


2

I would try to model the pre-treatment trends in various ways to see how sensitive the results are to those assumptions. Alternatively, you can explore a propensity-score-weighted DID. There are some examples here (in my answer and also the second link in the original question; both involve a simpler setup than you have with the variable treatment timing). ...


2

Looking at the help file of the pedroni99 function and Pedroni's 1999 paper (especially pages 665-666), we find that The standardized values of the test statistics are asymptotically normal (0,1) under $H_0$ and the null hypotheses seem are "No cointegration". If your sample is large enough to invoke asymptotic arguments, you can compare the test ...


2

Likely more context is needed to provide insight into the proposed analysis, but the general approach can be laid out: The task is to use time varying covariates to estimate the hazard ratio for death comparing groups differing by a "slope" of pharmacokinetic trend in the inflammatory marker. The Cox-model is a regression model that estimates ...


2

So if I understand this question correctly you are asking about adding controls in the DD. First, let us consider why one would do this. There are essentially two reasons, Reduce Error Variance Aid in Identification The first reason is simple enough. Adding in covariates helps to explain some of the variation in $Y$ and so reduces the variance in our ...


2

Because you have more free parameters than you do observations, hence there's no way to estimate their standard error. The model has free-parameters for: baseline, pre/post time, group indicator, the group by time interaction, and the standard error term. Consider for a normal model, you need just one observation to estimate the mean, two observations for ...


2

For the model: model1 <- lme(OUTCOME ~ time * X + Age + edu + gender, random=~time|ID, data=df) is the above one is correct It is consistent with the description in the question, yes. However, please note that it is common for the time variable to be centred in this type of modelling. From the description, there is no way to know if that did that. time:...


2

You can sometimes improve fit by: Getting more pre-treatment data when possible, though that runs the risk of going so far back that the structural relationship is too different from the period in the study, like when CA was Mexico. Also, does not always work. Adding variables that are not just the lagged outcome in calculating the weights, like beer ...


2

In addition to the other excellent answer (and yes, more data can really help, this could include different levels of aggregation, e.g. instead of state-level data, can you get county-level data?), there's also the option of shortening or weighting the time horizon for which you are matching the synthetic control. E.g. in the book example, they could have ...


2

I don't see why it should be one or the other. You can fit a beta GLM with fixed effects foor country, if that's what you want, though with 27 countries I would be inclined to fit random intercepts for country.


2

This is explained on p663-664 of Cole and Hernán (2008), another great resource on inverse probability weights. Adding covariates to the stabilization factor in the numerator removes the ability of the weights to balance those covariates. When covariates are included in the numerator, it is expected that the analyst will include those covariates in the ...


2

Your example look like longitudinal data (also called panel data), that is, many short time series. There is usually not a requirement with equispaced observations for longitudinal data models. On this site, look through panel-data. You could also, in your example, fill in the zeros. Then you have an intermittent time series, see intermittent-time-series. ...


2

In the first model: correct ~ 1 + trial * cue + (1 | ID:trial) + (1 + trial | ID) (1 | ID:trial) treats trial as a random factor that is nested within levels of ID. From the description in the question, this is not the case. Since all participants were in each trial, these would be crossed random effects, not nested. To understand the difference, see here: ...


2

As you have described the situation, what you have is a binomial regression model (total A versus not-A counts per teacher) with year of teacher graduation as the only predictor. Although you have an ID value for each teacher, you seem to have only 1 entry (cumulative counts) for each teacher rather than entries year-by-year, so that ID doesn't even need to ...


2

It is not really anything to do with trying to get a normal distribution (and in most models, you don't really need to transform variables to make them normal anyway). We generally apply a logarithmic transformation to a positive variable when it either grows or decays on an exponential scale (i.e., it grows/shrinks by a percentage that has a roughly fixed ...


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