Yes, it is absolutely possible to run a Structural Equation Model (SEM) that incorporates both latent variables (endogenous or exogenous) and observed exogenous variables. In fact, this is a very common setup in SEM applications across fields like psychology, sociology, education, and marketing, where you often have a mix of constructs that are indirectly measured (your latents like peer pressure or atmosphere, via their 5-6 items/indicators) and directly measured variables (your observed exogenous ones like income, age, and gender) that serve as predictors or covariates.

Thank you for your answer. Really appreciate it.

If you tend to know of any literature in support of this, can u please send. It would be really helpful. Thank you once again.

You can look into the literature on so-called multiple-indicator-multiple-cause (MIMIC) models, which use latent endogenous and observed exogenous variables:

Jöreskog, K. G., & Goldberger, A. S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American statistical Association, 70(351a), 631-639.

Article Estimation of a Model with Multiple Indicators and Multiple ...

Many general text books on SEM will also have a section or chapter on MIMIC models. For example:

https://www.oreilly.com/library/view/structural-equation-modeling/9781118356302/c03anchor-1.html

The observed exogeneous variables would not be part of the CFA/measurement model if they are single-indicator variables. The implicit assumption would be that the single-indicator exogenous variables are measured without measurement error (i.e., with perfect [1.0] reliability), which may or may not be a reasonable assumption for variables such as income, age, or gender.

SEM in general is perfectly flexible in handling a mix of observed and latent exogenous, endogenous, and/or mediator variables.

Regarding literature supporting the inclusion of both latent and observed (manifest) exogenous variables in SEM—where observed exogenous variables (like demographics or direct measures) typically enter the structural model directly without forming part of the measurement model or CFA—here are some key references from established sources in the field. These confirm the feasibility and common practice of such mixed models, often with examples or diagrams showing observed exogenous variables (e.g., as predictors) alongside latent constructs.

1. Brannick, M. T. (n.d.). Structural Equation Modeling (SEM). University of South Florida. Available at: http://faculty.cas.usf.edu/mbrannick/regression/SEM.html This resource provides a clear overview using LISREL notation, where observed exogenous variables (labeled as X) are directly incorporated into the structural model to influence latent endogenous variables, without requiring a measurement component for the observed ones themselves.

2. Stage, F. K., Carter, H. C., & Nora, A. (2004). Path analysis: An introduction and analysis using LISREL models. In Structural Equation Modeling (pp. 1-22). ResearchGate. This chapter distinguishes between latent and observed variables as exogenous or endogenous, noting that observed exogenous variables (e.g., gender as a control) are placed in the structural model as predictors, separate from the measurement model which focuses on latent constructs and their indicators.

3. Grace, J. B., Anderson, T. M., Olff, H., & Scheiner, S. M. (2010). On the specification of structural equation models for ecological systems. Ecological Monographs, 80(1), 67-87. Available via PMC: https://pmc.ncbi.nlm.nih.gov/articles/PMC3176611/ The authors explain that exogenous variables, which can be observed (manifest), are not explained within the model and are uncorrelated with disturbances, allowing them to serve as direct predictors in the structural part without needing measurement validation via CFA.

4. Little, T. D. (2013). Longitudinal Structural Equation Modeling. Guilford Press. (See chapters on model specification.) While not directly from the search, this is a standard reference that builds on Kline’s work, illustrating models where observed exogenous covariates (e.g., age, income) are regressed onto latent endogenous variables in the structural equations, bypassing the measurement model since they lack indicators.

5. For a practical software-focused guide: SAS Institute. (2016). Introduction to Structural Equation Modeling with Latent Variables. SAS/STAT 14.2 User’s Guide. Available at: https://support.sas.com/documentation/onlinedoc/stat/142/introcalis.pdf This document includes examples (e.g., career aspiration data) where observed exogenous variables (like parental aspiration scores) are directly used as predictors in path models, integrated into the structural relationships without separate measurement modeling unless error is explicitly added.

Additionally, foundational textbooks like Rex B. Kline’s Principles and Practice of Structural Equation Modeling (5th ed., 2023, Guilford Press) extensively cover this in chapters on model specification (e.g., Chapter 7), with path diagrams showing observed exogenous variables directly influencing latents. If you have access via a library or academic database, I recommend starting there for detailed examples.