cancel
Showing results for 
Show  only  | Search instead for 
Did you mean: 
JMP is taking Discovery online, April 16 and 18. Register today and join us for interactive sessions featuring popular presentation topics, networking, and discussions with the experts.
Choose Language Hide Translation Bar
Steve_Kim
Level III

Percentile & Goodness-of-fit of Zero Inflated Negative Binomial (ZINB) and Negative Binomial (NB)

Hi All,

 

(1) I'd like to get the goodness-of-fit of of Zero Inflated Negative Binomial (ZINB) and Negative binomial (NB) distribution from the following dataset.

(2) I also want to calculate the 95th percentile from the each distribution (ZINB & NB)  with JMP 14 or JMP 14 Pro

(3) Is it possible to plot the density functions of ZINB & NB against empirical density of simulated data ?  (Y:Cumulative Probability, X:counts)

Thanks in advance.  : )

 

 

 

Sample No.Data
10
20
30
40
50
60
70
80
90
100
110
120
130
140
152
160
170
180
190
200
210
220
230
240
250
261
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
544
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
702
710
720
730
740
750
760
770
780
790
800
810
820
830
840
850
860
870
880
890
900
910
920
930
940
950
960
970
980
990
1000
1010
1020
1030
1040
1050
1060
1070
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
1211
1220
1231
1240
1250
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1411
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1592
1600
1610
1620
1630
1640
1650
1660
1670
1680
1690
1700
1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1971
1 ACCEPTED SOLUTION

Accepted Solutions

Re: Percentile & Goodness-of-fit of Zero Inflated Negative Binomial (ZINB) and Negative Binomial (NB)

I would normally use the Distribution platform to fit such models but the negative binomial distribution is not one of the choices. Here I modelled your data with the gamma Poisson distribution, obtained the goodness-of-fit test statistics, and estimated the 95% quantile:

 

Screen Shot 2019-04-09 at 7.52.00 AM.png

 

It seems to do well.

 

The negative binomial and zero-inflated negative binomial distribution models are available in the JMP Pro Generalized Regression platform. I used an intercept-only linear predictor to get these results:

 

Screen Shot 2019-04-09 at 8.01.12 AM.png

 

Screen Shot 2019-04-09 at 8.02.51 AM.png

 

The AICc suggests that the gamma Poisson distribution is one of the best fits to the data.

View solution in original post

4 REPLIES 4

Re: Percentile & Goodness-of-fit of Zero Inflated Negative Binomial (ZINB) and Negative Binomial (NB)

I would normally use the Distribution platform to fit such models but the negative binomial distribution is not one of the choices. Here I modelled your data with the gamma Poisson distribution, obtained the goodness-of-fit test statistics, and estimated the 95% quantile:

 

Screen Shot 2019-04-09 at 7.52.00 AM.png

 

It seems to do well.

 

The negative binomial and zero-inflated negative binomial distribution models are available in the JMP Pro Generalized Regression platform. I used an intercept-only linear predictor to get these results:

 

Screen Shot 2019-04-09 at 8.01.12 AM.png

 

Screen Shot 2019-04-09 at 8.02.51 AM.png

 

The AICc suggests that the gamma Poisson distribution is one of the best fits to the data.

Steve_Kim
Level III

Re: Percentile & Goodness-of-fit of Zero Inflated Negative Binomial (ZINB) and Negative Binomial (NB)

Thank you Mark!
And..Can I get more your advice? :)

If the other dataset is matched with ZINB or NB, I need to calculate 95th percentile and 99th percentile from that distribution per the guidance.
(1) Is it possible to get these percentiles from the JMP Pro Generalized Regression platform or other way?
(2) If the dataset is not fitted well with Poisson or NB (maybe i can check it with GammaPoisson), I hv to check goodness of fit for ZINB. Is there a way to check it visually (Q-Q plot) or with other method except AIC or BIC?
Many thanks!

Re: Percentile & Goodness-of-fit of Zero Inflated Negative Binomial (ZINB) and Negative Binomial (NB)

1.) You use the parameter estimates for either the ZINB or NB distribution model to estimate the 95% percentile from the inverse cumulative distribution function.

 

2.) AIC and BIC are criteria for model selection. They do not assess goodness of fit. JMP does not have a Q-Q plot for these distributions that I know of. They exist in the Distribution platform for the gamma Poisson, though.

Steve_Kim
Level III

Re: Percentile & Goodness-of-fit of Zero Inflated Negative Binomial (ZINB) and Negative Binomial (NB)

Thank you for the clear answer :)