Classroom context and climate are inherently classroom-level (L2) constructs, but applied researchers sometimes--inappropriately--represent them by student-level (L1) responses in single-level models rather than more appropriate multilevel models. Here we focus on important conceptual issues (distinctions between climate and contextual variables; use of classroom L2 rather than student-level L1 measures) and more appropriate multilevel models. To illustrate these issues, we consider the effects of two L2 classroom climate variables and one L2 classroom contextual variable on two L1 student-level outcomes for 2261 students in 128 classes. Through this example, we illustrate how to apply evolving doubly latent multilevel models to (a) evaluate the factor structure of L1 and L2 constructs based on multiple indicators of classroom climate and context measures, (b) control measurement error at L1 and L2, (c) control sampling error in the aggregation of L1 responses to form L2 constructs (the average of student-level responses to form classroom-level constructs), and (d) provide guidelines for appropriate analysis of classroom climate as an L2 construct. (Contains 2 footnotes, 2 tables and 1 figure.)