Regression: Independent variable (proportions) with missing values

#1
Hello,

My dependent variable is counts of fights in schools. My independent variable is the schools’ proportion of students with a single parent. I hypothesized that schools with higher proportion of students with only one parent will have more fights. I used a negative binomial regression. The problem starts when I another covariate variable was included; this variable is type of school: public vs private. Public schools have the entire range on proportion of students with single parents (ex. some schools have 10% ,50% 100% of students with only one parent) but private schools only have up to 14% of students with single parents. That is, none of my private schools have a proportion of students with only one parent of 15% +. So let say that I want to regress fights on single parents just for private schools (remember that private schools only have values up to 14%).

1. How this model (negative binomial) or even a linear regression (assuming my dependent variable is continuous) will generate the predicted probabilities if there is not proportions in the higher scale? Below if an example of my predicted probabilities. AS you see the last values are flat at the end. How can I explain this?
2. How this missing data will affect my regression?


Code:
YearFight	IRR	Std. Err.	z	P>z	[95% Conf.	Interval]
						
parent	1.015338	.0024643	6.27	0.000	1.01052	1.02018
type	.6455384	.3093906	-0.91	0.361	.2523262	1.651513
_cons	9.868429	4.540015	4.98	0.000	4.005427	24.31348
						
/lnalpha	3.047319	.0551019			2.939321	3.155317
						
alpha	21.05881	1.160381			18.90301	23.46046
Code:
YearFight	IRR	Std. Err.	z	P>z	[95% Conf.	Interval]
						
parent	.9248385	.1295676	-0.56	0.577	.7027724	1.217074
_cons	15.39693	13.27548	3.17	0.002	2.84128	83.43609
						
/lnalpha	3.057227	.2470003			2.573116	3.541339
						
alpha	21.2685	5.253328			13.1066	34.5131