Engaging in interactions with peers is important for student learning. Many studies have quantified patterns of student interactions in in-person physics courses using social network analysis, finding different network structures between instructional contexts (lecture and laboratory) and styles (active and traditional). Such studies also find inconsistent results as to whether and how student-level variables (e.g., grades and demographics) relate to the formation of interaction networks. In this cross-sectional research study, we investigate these relationships further by examining lecture and lab interaction networks in four different remote physics courses spanning various instructional styles and student populations. We apply statistical methods from social network analysis--exponential random graph models--to measure the relationship between network formation and multiple variables: students' discussion and lab section enrollment, final course grades, gender, and race or ethnicity. Similar to previous studies of in-person courses, we find that remote lecture interaction networks contain large clusters connecting many students, while remote lab interaction networks contain smaller clusters of a few students. Our statistical analysis suggests that these distinct network structures arise from a combination of both instruction-level and student-level variables, including the learning goals of each instructional context, whether assignments are completed in groups or individually, and the distribution of gender and major of students enrolled in a course. We further discuss how these and other variables help to understand the formation of interaction networks in both remote and in-person physics courses.