Trying Latex

[Steve Samuels]

\[
\; \; \alpha + \beta = \gamma \quad \quad \quad \quad (1) \\
\delta + \epsilon = \Omega \quad \quad \quad \quad
\]

[Steve Samuels]

A test that \(\sigma=0\) makes no sense except for higher levels of multi-level data. The he standard test when there are inequality constraints (e.g.\(\sigma \ge 0\))is based on the chi-bar square distribution. See page 14 of the Multi-level Mixed Effects manual, which states:

When there is only one variance being set to 0 in the reduced model, the asymptotic distribution of the LR test statistic is a 50:50 mixture of a \(\chi_p^2\) and a \(\chi_{p+1}^2\)
distribution, where p is the number of other restricted parameters in the reduced model that are unaffected by boundary conditions. Stata labels such test statistics as chibar and adjusts the significance levels accordingly.

[skolenik]

Isn't that denoted $\bar\chi^2$?

Hm... there must be more to it than what my eyes see here. How do you format it so that it is rendered as \LaTeX?

[Maarten Buis]

You can see the raw code from another post by pressing the Quote button at the bottom of that post.

[skolenik]

Oh, so it needs to be \(\bar\chi^2\), then? It still does not seem to work. Am I asking for something too complicated? Does \(\chi^2_p\) work, at least? Is there an FAQ about this?

[Steve Samuels]

I agree there's a need for an FAQ about exactly what subset of Latex the Forum will accept. http://docs.mathjax.org/en/latest/tex.html shows functionality that doesn't seem to work on the forum, e.g. "$ $" delimiters and numbered equations. I'll ask on the other Forum.

[Kieran McCaul]

\[
Var(X) = \sum_{i=1}^n p_i\cdot(x_i - \mu)^2 = \sum_{i=1}^n (p_i\cdot x_i^2) - \mu^2
\]

[Kieran McCaul]

Does this work: \(\lambda\). How about this \( A \) or \(A\)

[Steve Samuels]

\(
\quad P_{all} = W P_r + (1-W)P_{nr} \\
P_{all}- P_r = (1-W)(P_r - P_{nr}) \\
\)


\(
\quad P_{all} = W P_r + (1-W)P_{nr} \\
P_{all}- P_r = (1-W)(P_r - P_{nr}) \\
\)

[Steve Samuels]

As you may have seen when you registered, using full names is Statalist etiquette; see also section 6 of the FAQ http://www.statalist.org/forums/help. I prefer not to work with posters whose full names I don't know. So for any follow-up posts, please change your user name to your full name-just click the "contact us" button on the bottom right of the page.


You have a more serious issue than that of weights. The events variable in the standard error formula is the number of observed events, which are whole numbers. Many of your tabled numbers are fractional, and it is not a coincidence that these defective versions occur when the person-years is 100,000. The tabled numbers of "events" for those groups are actually are the numbers of events per 100,000 person-years.


$$
IR= \frac{Events}{T}
$$

which is in units events per person-years.

Then one delta-method based approximation for the standard error of the log incidence rate is:

$$
\text{se}(log(IR)) =(1/Events)^.5 \quad \quad \quad (1)
$$

This is the basis of the formula you quote for the standard error of a log incidence rate ratio in two populations

$$
\text{se(log(\left(\frac{IR_1}{IR_0}\right) =
$$
$$
\text{log}(IR_1) -\text{log}(IR_0)=(1/\text{Events}_1 +1/\text{Events}_2)^.5 \quad \quad \quad (2)
$$

But that the events in equation (1) and (2) must be the number of observed events, i.e. whole numbers. The fractional numbers of events in your table are therefore not the right numbers for calculating standard errors It is not a coincidence that these fractional occur when the person-years is 100,000.

Here is how that happened. I'll use an example for a single incidence rate. Suppose Events = 12 and $T$ = 43,332 person- years. Then the incidence rate is

$$
IR= \frac{12}{43332} = 0.0002769316 \text{ events per person-year}
$$


However person-years this is the wrong units. We want events per 100,000 person years. To get this incidence rate, call it $IR_*$, we must multiply by 100,000. So that the result is:

$$
IR_*= 27.69 \text{ events per 100,000 person-years}
$$

So you can see that in every line where you have a fractional number of events, all you have is the value of the incidence rate per 100,000 person-years, not the actual number of observed events. So those standard error calculations are completely wrong.

If you cannot recover the actual numbers of events or person-years for study 2, you won't be able to use it in your meta-analyses. Likewise, you can't use the number of events in the "standard population" group for standard error calculations. (You may not need to if the numbers of events in those populations are big enough.)

There are other issues, but where you go next depends on the details that you can recover.

I am happy to have helped you so far. However as you read on the page where you registered, Statalist etiquette is to use full real names. (See also section 6 of the Statalist FAQ http://www.statalist.org/forums/help.) I really don't care to engage with posters whose full names I don't know, so I request that you change your user-name to your full real name. Tap the "Contact Us" button at the bottom of the page. I hope that you will do this, but if you choose not to, I'll not respond to further posts from you..

[daniel klein]

\[
y = \beta * X + \epsilon
\]

[Roberto Liebscher]

Does this work? \; \; E=mc^2

[Roberto Liebscher]

Does this work? $ E=mc^2 $

Unfortunately not. Maybe:

\[
E=mc^2
\]

Another try:
$$
E=mc^2
$$

What's wrong with my examples?

[bsc.j.j.w]

$$var_{i}$$

[Konrad Zdeb]

How about this: $$x=\frac{1+y}{1+2z^2}$$