# Panel Count Models with Random Effects and Sample Selection" In PanelCount: Random Effects and/or Sample Selection Models for Panel Count Data

round(m2$estimates, digits=3)  The estimate of x is still biased because the above model fails to consider the sample selection issue in the true DGP. ### 3.3. ProbitRE m3 = ProbitRE(z~x+w, data=sim, id.name='id', verbose=-1) round(m3$estimates, digits=3)


The specification of this model is consistent with the DGP of the first stage. Therefore, it can produce consistent estimates of the parameters in the first stage.

### 3.4. ProbitRE_PoissonRE

m4 = ProbitRE_PoissonRE(z~x+w, y~x, data=sim, id.name='id', verbose=-1)
round(m4$estimates, digits=3)  The results above the second "(Intercept)" are for the first stage. After accounting for self-selection at the individual level, the estimate of x in the second stage is still biased because the true DGP also includes self-selection at the individual-time level. ### 3.5. ProbitRE_PLNRE # The estimation may take up to 1 minute m5 = ProbitRE_PLNRE(z~x+w, y~x, data=sim, id.name='id', verbose=-1) round(m5$estimates, digits=3)


The results above the second "(Intercept)" are for the first stage. The specification of this model is consistent with the true DGP and hence the estimate of x is very close to its true value 1.

The estimation of ProbitRE_PoissonRE and ProbitRE_PLNRE does not require a variable like w that exclusively influences the first-stage outcome, but the identification is stronger with such a variable.

## Citations

Peng, J., & Van den Bulte, C. (2022). Participation vs. Effectiveness in Sponsored Tweet Campaigns: A Quality-Quantity Conundrum. Available at SSRN: https://www.ssrn.com/abstract=2702053

Peng, J., & Van Den Bulte, C. (2015). How to Better Target and Incent Paid Endorsers in Social Advertising Campaigns: A Field Experiment. 2015 International Conference on Information Systems. https://aisel.aisnet.org/icis2015/proceedings/SocialMedia/24/

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PanelCount documentation built on Oct. 7, 2022, 9:05 a.m.