Respondent-driven sampling (RDS) is a network sampling method commonly used to access hidden populations, such as those at high risk for HIV/AIDS and related diseases, in situations where sampling frames do not exist and conventional sampling techniques are not possible. In RDS, participants recruit their peers into the study, which has proven effective as an enrollment strategy but requires careful statistical analysis when making inference about the population. Data from RDS surveys inform key policy and resource allocation decisions, and in particular population size estimates are essential to understand counts of at-risk individuals to develop counseling and treatment programs and monitor health needs and epidemics. Successive sampling population size estimation (SS-PSE) is a commonly used method to estimate population size from RDS surveys, in which the decrease in social network size of participants over the study period is used to gauge the sample fraction. However, SS-PSE relies on self-reported social network sizes, which are subject to missingness, misreporting, and bias, and it is not robust to extreme values. In this talk, we present a modification to the SS-PSE methodology that jointly models the effective social network size of each individual along with the population size in a Bayesian framework. The model for effective network size, which we call visibility to reflect its usage as a proxy for inclusion probability, incorporates a measurement error model for self-reported social network size, as well as the number of recruits an individual was able to enroll and the time they had to recruit. We present and assess the imputed visibility SS-PSE framework, and demonstrate its utility using an RDS study of people who inject drugs (PWID) from Kosovo.