Table of Contents
The process of manually generating predicted counts from a ZIP or ZINB model involves using the parameter estimates obtained from the model to calculate the expected number of counts for a given dataset. This can be done by first determining the probability of a count being equal to zero, and then using a combination of the remaining probabilities and the estimated dispersion parameter to calculate the expected count for each observation. This method allows for a deeper understanding of the model’s predictions and can be useful in validating the effectiveness of the model.
How can I manually generate the predicted counts from a ZIP or ZINB model based on
the parameter estimates? | Stata FAQ
This page shows some examples on how to generate the predicted count from
a zero-inflated Poisson or a zero-inflated negative binomial model based on
the parameter estimates. Zero-inflated models allow us to model two
processes simultaneously. Let’s take ZIP as an example. Basically, zero
outcome arises from two different processes. In one process, the outcome is
always zero and in the other process, zero outcome, as well as other
outcomes obey the Poisson process. With the two parts
of the model, how do we generate the predicted count after running the
model? The examples demonstrate the steps to this end.
Example 1. Zero-inflated Poisson model with logit inflation model
webuse fish, clear
zip count persons livebait, inf(child camper) nolog
Zero-inflated Poisson regression Number of obs = 250
Nonzero obs = 108
Zero obs = 142
Inflation model = logit LR chi2(2) = 506.48
Log likelihood = -850.7014 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
count |
persons | .8068853 .0453288 17.80 0.000 .7180424 .8957281
livebait | 1.757289 .2446082 7.18 0.000 1.277866 2.236713
_cons | -2.178472 .2860289 -7.62 0.000 -2.739078 -1.617865
-------------+----------------------------------------------------------------
inflate |
child | 1.602571 .2797719 5.73 0.000 1.054228 2.150913
camper | -1.015698 .365259 -2.78 0.005 -1.731593 -.2998038
_cons | -.4922872 .3114562 -1.58 0.114 -1.10273 .1181558
------------------------------------------------------------------------------
predict pThe variable p created above is the predicted count based on this model.
Now we show the steps to create the same p using the parameter
estimates. Basically, it has two parts, the model for the usual Poisson
process and the model for the process of zeros. Variable a1 below is
the linear prediction based on the first model and variable a2 is the
linear prediction for the second model which is a logit model by default.
Variable pzero is the predicted probability for being in the first
process which only produces zero count. Variable pcount is then the
predicted count based on the two processes.
gen a1 = -2.178472 + .8068853*persons + 1.757289*livebait
gen a2 = -.4922872 + 1.602571*child -1.015698*camper
gen pzero = exp(a2)/(1+exp(a2))
gen pcount = exp(a1)*(1-pzero) /*for logit model*/
sum p pcount
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
p | 250 2.770999 3.269588 .079269 13.55015
pcount | 250 2.770997 3.269585 .0792689 13.55014
Example 2. Zero-inflated Poisson model with probit inflation model
The only difference between this example and the previous one is that the
inflation part in this one is modeled by probit model instead of logit
model.
webuse fish, clear
zip count persons livebait, inf(child camper) probit nolog
Zero-inflated Poisson regression Number of obs = 250
Nonzero obs = 108
Zero obs = 142
Inflation model = probit LR chi2(2) = 506.29
Log likelihood = -850.3968 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
count |
persons | .8062521 .0453179 17.79 0.000 .7174306 .8950736
livebait | 1.755824 .2444357 7.18 0.000 1.276739 2.234909
_cons | -2.174616 .2858538 -7.61 0.000 -2.734879 -1.614353
-------------+----------------------------------------------------------------
inflate |
child | .9658273 .1576773 6.13 0.000 .6567855 1.274869
camper | -.6112131 .2146819 -2.85 0.004 -1.031982 -.1904442
_cons | -.295569 .1869964 -1.58 0.114 -.6620753 .0709372
------------------------------------------------------------------------------
predict p
gen a1 = -2.174616 + .8062521*persons + 1.755824 *livebait
gen a2 = -.295569 + .9658273*child -.6112131*camper
gen pzero = normal(a2) /*for probit model*/
gen pcount = exp(a1)*(1-pzero)
sum p pcount
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
p | 250 2.754194 3.272803 .0649889 13.53128
pcount | 250 2.754194 3.272803 .0649889 13.53128
Example 3. Zero-inflated negative binomial model with logit inflation model
Now we switch to zero-inflated negative binomial model. The way to
calculate the predicted values is exactly the same as for zero-inflated
Poisson models.
webuse fish, clear
zinb count persons livebait, inf(child camper) nolog
Zero-inflated negative binomial regression Number of obs = 250
Nonzero obs = 108
Zero obs = 142
Inflation model = logit LR chi2(2) = 82.23
Log likelihood = -401.5478 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
count |
persons | .9742984 .1034938 9.41 0.000 .7714543 1.177142
livebait | 1.557523 .4124424 3.78 0.000 .7491503 2.365895
_cons | -2.730064 .476953 -5.72 0.000 -3.664874 -1.795253
-------------+----------------------------------------------------------------
inflate |
child | 3.185999 .7468551 4.27 0.000 1.72219 4.649808
camper | -2.020951 .872054 -2.32 0.020 -3.730146 -.3117567
_cons | -2.695385 .8929071 -3.02 0.003 -4.44545 -.9453189
-------------+----------------------------------------------------------------
/lnalpha | .5110429 .1816816 2.81 0.005 .1549535 .8671323
-------------+----------------------------------------------------------------
alpha | 1.667029 .3028685 1.167604 2.380076
------------------------------------------------------------------------------
predict p
gen a1 = -2.730064 + .9742984*persons + 1.557523*livebait
gen a2 = -2.695385 + 3.185999*child -2.020951*camper
gen pzero = exp(a2)/(1+exp(a2))
gen pcount = exp(a1)*(1-pzero)
sum p pcount
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
p | 250 3.131795 4.189243 .0159387 15.11586
pcount | 250 3.131795 4.189243 .0159391 15.11586
Example 4. Zero-inflated Poisson model with logit inflation model again:
general setup
In previous examples, we have manually generated these variables using
the parameter estimates. In this example, we make use of the Stata’s stored
matrix for parameter coefficients. This is the general and more useful
approach in practice.
webuse fish, clear
zip count persons livebait, inf(child camper) nolog
Zero-inflated Poisson regression Number of obs = 250
Nonzero obs = 108
Zero obs = 142
Inflation model = logit LR chi2(2) = 506.48
Log likelihood = -850.7014 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
count |
persons | .8068853 .0453288 17.80 0.000 .7180424 .8957281
livebait | 1.757289 .2446082 7.18 0.000 1.277866 2.236713
_cons | -2.178472 .2860289 -7.62 0.000 -2.739078 -1.617865
-------------+----------------------------------------------------------------
inflate |
child | 1.602571 .2797719 5.73 0.000 1.054228 2.150913
camper | -1.015698 .365259 -2.78 0.005 -1.731593 -.2998038
_cons | -.4922872 .3114562 -1.58 0.114 -1.10273 .1181558
------------------------------------------------------------------------------
predict p
matrix list e(b)
e(b)[1,6]
count: count: count: inflate: inflate: inflate:
persons livebait _cons child camper _cons
y1 .80688527 1.7572894 -2.1784716 1.6025705 -1.0156983 -.49228716
gen a1 = _b[count:_cons] + _b[count:persons]*persons + _b[count:livebait]*livebait
gen a2 = _b[inflate:_cons] + _b[inflate:child]*child +_b[inflate:camper]*camper
gen pzero = exp(a2)/(1+exp(a2))
gen pcount = exp(a1)*(1-pzero) /*for logit model*/
sum p pcount
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
p | 250 2.770999 3.269588 .079269 13.55015
pcount | 250 2.770999 3.269588 .079269 13.55015
Cite this article
stats writer (2024). How can I manually generate the predicted counts from a ZIP or ZINB model based on the parameter estimates?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/how-can-i-manually-generate-the-predicted-counts-from-a-zip-or-zinb-model-based-on-the-parameter-estimates/
stats writer. "How can I manually generate the predicted counts from a ZIP or ZINB model based on the parameter estimates?." PSYCHOLOGICAL SCALES, 1 Jul. 2024, https://scales.arabpsychology.com/stats/how-can-i-manually-generate-the-predicted-counts-from-a-zip-or-zinb-model-based-on-the-parameter-estimates/.
stats writer. "How can I manually generate the predicted counts from a ZIP or ZINB model based on the parameter estimates?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/how-can-i-manually-generate-the-predicted-counts-from-a-zip-or-zinb-model-based-on-the-parameter-estimates/.
stats writer (2024) 'How can I manually generate the predicted counts from a ZIP or ZINB model based on the parameter estimates?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/how-can-i-manually-generate-the-predicted-counts-from-a-zip-or-zinb-model-based-on-the-parameter-estimates/.
[1] stats writer, "How can I manually generate the predicted counts from a ZIP or ZINB model based on the parameter estimates?," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, July, 2024.
stats writer. How can I manually generate the predicted counts from a ZIP or ZINB model based on the parameter estimates?. PSYCHOLOGICAL SCALES. 2024;vol(issue):pages.