Dynamically typed vector languages are popular in data analytics and statistical computing. In these languages, vectors have both dynamic type and dynamic length, making static generation of efficient machine code difficult. In this paper, we describe a trace-based just-in-time compilation strategy that performs partial length specialization of dynamically typed vector code. This selective specialization is designed to avoid excessive compilation overhead while still enabling the generation of efficient machine code through length-based optimizations such as vector fusion, vector copy elimination, and the use of hardware SIMD units. We have implemented our approach in a virtual machine for a subset of R, a vector-based statistical computing language. In a variety of workloads, containing both scalar and vector code, we show near autovectorized C performance over a large range of vector sizes.