Dear statalist,
First of all, I would like to thank you all for the valuable information you are providing, and which is actually contributing to our knowledge.
I have 3 questions please and I hope that it will be answered.

I am using unbalanced panel data for a set of companies, and I want to apply the (Discrete hazard proportional odds model).
In 2005 set of standards have been issued and therefore companies were becoming under risk, since 2005, to adopt these standards as the adoption is voluntary. However, due to the lack of financial reports of many companies in 2005, and most of the annual reports appeared in 2006, I decided that the period of the study will be from 2006 to 2015. If I started since 2005 then all companies that established in 2006 will be considered as a (left-truncated) (i.e. any newly established company after 2005 will be under risk to adopt “the subjects have been at risk before entering the study”). And I want to minimize the left-truncated observation as much as possible because they should be excluded when conducting the unobserved heterogeneity “Frailty”. However, they will not be excluded from the sample when conducting the discrete hazard model without Frailty. Therefore, the study period will be from 2006-2015.
My Questions:
  1. Based on the above case, does my understanding of the meaning of left-truncated observation is correct?
  2. Regarding the calendar time, companies calendar time’s will be coded (1) since 2006 and (2) in 2007 and (3) in 2008, and (4) in 2009 and so on until they experience the event. However, for left-truncated companies, they will be coded based on the year they issued. For instance, if a company issued in 2008 then the code for the calendar time for this company this year will be started from (3) not (1). Am I, right?
  3. I have deleted all the left-truncated observation to conduct the “Frailty” and the results showed me that the probability of the likelihood is not significant. However, I did run the analysis with them and the results showed me that the probability of the likelihood is not significant as well. So, that means the unobserved heterogeneity is negligible in my case??
I am very, very sorry for the length of the questions, but I hope that it will be answered, and I will be very grateful for you.
Million thanks in advance.