1. The National Science Foundation (NSF) is encouraging students to seek academic degrees and careers in science, mathematics, and engineering in the United States. Research has shown a gender difference in science, mathematics, and engineering participation. A key area of study is to investigate what factors influence these gender differences. A latent variable model is hypothesized to investigate factors that influence gender differences because previous research indicated variables such as characteristics of students in science, mathematics, and engineering.
A structural equation model with two exogenous latent variables measured by six observed variables is hypothesized to predict two endogeneous latent variables measured by five observed variables. The first independent latent variable, $\xi_1=$ Family Background, is measured by three variables: $X_1=$ family income, $X_2=$ father's education, and $X_3=$ mother's education. The other independent latent variable, $\xi_2=$ Encouragement, is measured by three variables: $X_4=$ personal encouragement, $X_5=$ institutional characteristics, and $X_6=$ admission status. Students' characteristics, $\eta_1=$ Students' Characteristics, is measured by three variables: $Y_1=$ cognitive abilities, $Y_2=$ interpersonal skills, and $Y_3=$ motivation. The other endogenous variable, $\eta_2=$ Aspirations, is measured by two variables: $Y_4=$ occupational aspiration and $Y_5=$ educational aspiration.
The hypothesized structural equation model represents a two-step approach: measurement (confirmatory factor analysis) and structural model. The structural model depicts the relationships between four latent variables: $\xi_1=$ Family Background, $\xi_2=$ Encouragement, $\eta_1=$ Students' Characteristics, and $\eta_2=$ Aspirations. The structural model is
$$
\begin{aligned}
\text { Students' Characteristics }= & \text { Family Background }+ \text { Encouragement } \\
& + \text { Aspirations }+ \text { error }
\end{aligned}
$$
Students' Characteristics $=$ Family Background + Encouragement
Aspirations $=$ Family Background + Encouragement + error .
With this information, you should be able to do the following:
. Diagram the structural equation model.