For the initial values <math>\{y_{i,0}\}^N_{i-1}</math>, there are two different ways to treat them in the construction of the likelihood function: treating them as constant, or imposing a distribution on them and calculate out the unconditional likelihood function. But whichever way is chosen to treat the initial values in the likelihood function, we cannot get rid of the integration inside the likelihood function when estimating the model by maximum likelihood estimation (MLE). Expectation Maximum (EM) algorithm is usually a good solution for this computation issue.<ref>For more details, refer to: {{cite book |last1=Cappé |first1=O. |last2=Moulines |first2=E. |last3=Ryden |first3=T. |year=2005 |title=Inference in Hidden Markov Models |publisher=Springer-Verlag |___location=New York |chapter=Part II: Parameter Inference |isbn=9780387289823 |chapter-url=https://books.google.com/books?id=4d_oEYn8Fl0C&pg=PA347 }}</ref> Based on the consistent point estimates from MLE, Average Partial Effect (APE)<ref>{{cite book |last=Wooldridge |first=J. |year=2002 |title=Econometric Analysis of Cross Section and Panel Data |url=https://archive.org/details/econometricanaly0000wool |url-access=registration |publisher=MIT Press |___location=Cambridge, Mass |page=[https://archive.org/details/econometricanaly0000wool/page/22 22] |isbn=9780262232197 }}</ref> can be calculated correspondingly.<ref> For more details, refer to: {{cite journal |first=Takeshi |last=Amemiya |year=1984 |title=Tobit models: A survey |journal=Journal of Econometrics |volume=24 |issue=1–2 |pages=3–61 |doi=10.1016/0304-4076(84)90074-5 }}</ref>
