I am analyzing the effect of two randomized interventions on 1) first-time and, 2) second-time event attendance. All variables are binary (0 vs. 1). Second attendance was conditional on first attendance. A large percentage (~50%) of people did not show up for first attendance; an even smaller percentage of first-time attendees (~50%*~20% = 10%) showed up the second time.   Intervention one was designed to increase both attendances; intervention two, just second attendance. Neither increased the probability of first or second attendance, but the interaction between second attendance and intervention was significant for both. The probability of second attendance was greater for both interventions relative to first.    The issue is that we are trying to test the effect of both interventions on second attendance *given* first attendance. We are also controlling for household using a random intercept.   I was advised an instrumental variable (IV) analysis would adjust for first attendance (Sussman BJ, Hayward, RA, BMJ, 2010). I regressed first attendance on intervention controlling for household, and then regressed second attendance on the predicted probability of first attendance (the instrument variable). I did this separately for both interventions, and the instrument variable was significant for both. My questions are:   Is IV appropriate given both interventions have a non-significant association to first attendance? I've read the instrument variable (randomized intervention), should be related to the treatment/biomarker (first attendance). If appropriate, how do I interpret the instrument variable coefficients?  Are there better analyses which measure second attendance for first-time attendees only? ... View more

I have a dataset with 71 million household ids that are associated with 73 million people. The issue is that each person can have a differing number of multiple house ids.  For example:   person_id house_id 1 1 1 2 1 3 2 2 3 2 3 3 4 1 4 3 5 6 5 4 5 5 6               6 6               4 What is the best way to figure out which people belong to the same house? In the above example house id 1 would include person Ids 1-4 because they belong to household Ids 1-3. House Id 2 would include person Ids 5-6, because they  belong to household Ids 4-6. I would like the data to look like this:    house_id person_one person_two person_three person_four 1 1 2 3 4 2 5 6 . . Ideally there would be one, unique house Id per row (which subsumes all house Ids that correspond to the same people). Each column is person 1, person 2, person 3, etc. associated with that house Id.  ... View more

I used proc nlmixed to implement a left-censored (aka Tobit), knotted spline, mixed effects regression. V1 is time in weeks relative to the intervention start (-33 to 34), and V2 is a truncated time variable in weeks with a knot at the intervention start (0 to 34). The outcome, log_y, is the log of a medication dosage with a range from 3.2 to 8.05. The data is organized as the average weekly medication dosage per-clinician. Many clinicians have average weekly dosages of 0, which is why we used a left-censored regression.  proc nlmixed data=mydat XTOL=1E-12 method=GAUSS qpoints=100; parms b0=1.6 b1=-.04 b2=-.5 sigma2_u=2 sigma2=5; bounds sigma2_u sigma2 >=0; pi = constant("pi"); mu = b0 + b_0j + b1*v1 + b2*v2; if log_y > 0 then ll = (1 / (sqrt(2*pi*sigma2))) * exp( -(log_y-mu)**2 / (2*sigma2) ); if log_y = 0 then ll = probnorm( (log_y - mu) / sqrt(sigma2) ); L = log(ll); model log_y ~ general(L); random b_0j ~ normal(0, sigma2_u) subject=id; run; quit; Everything worked fine; the probability density function and cumulative density function were used on uncensored and censored obs. respectively to achieve the maximum log likelihood. Here are the estimates: b0: -12.65 b1: -0.03 b2: -0.01 sigma2_u: 9.02 sigma1: 85.49 But then a colleague told me I need adjust the coefficients to convert to OLS scale according to Wooldridge (Chapter 17.2, pages 596-601) found here: https://economics.ut.ac.ir/documents/3030266/14100645/Jeffrey_M._Wooldridge_Introductory_Econometrics_A_Modern_Approach_2012.pdf   My questions are:   1. Is this necessary if the algorithm accounted for censored obs. by using the cumulative density function to maximize the likelihood?    2. If this is necessary, the average partial effect (APE), is the scale factor. The equation occurs in the second sentence in paragraph five on page 600. My interpretation is that it's each predicted value for every level of x divided by sigma, summed, and divided by one. As an example with limited obs.:   intercept V1 coef_V1 V2 coef_V2 xi(b) sigma (xi(b))/sigma sum (1/sum) APE -12.65 -1 -0.03 0 -0.01 -12.62 85.49 -.1476 -0.444 1/-.444 -2.3 -12.65 0 -0.03 0 -0.01 -12.65 85.49 -.1479 -12.65 1 -0.03 1 -0.01 -12.69 85.49 -.1484   Is this correct?   3. According to Wooldridge in the second paragraph on page 599 just below equation 17.26, the adjustment factor (xb/sigma) can be achieved by plugging in the maximum likelihood estimates, and is always between 0 and 1. This obviously wasn't true for me because I have negative estimates. Then I saw in table 17.2 (pg. 601) two types of estimates, Tobit and MLE. What is the difference between these estimates? Why are the Tobit estimates negative, and the MLE positive? Plugging in                                          positive MLE estimates would result in a pos. adjustment factor between 0 and 1, so that makes sense, I just don't understand the difference. My first thought was that the MLEs are from a maximum likelihood regression on just uncensored obs., whereas the tobit incorporates censored obs (and can therefore have negative estimates). If this is the case, that brings me back to my original question, is the adjustment even necessary if using proc nlmixed?     ... View more