Does my response meet the definition for factor loadings? $$Correlations are between two variables, with factor loadings as the representation of the one variable upon all variables assessed as one $$unobserved concept.$$ Causal Analytics Program $($CAP$)$

Should I keep the diagram or remove it from the answer?

How should the CFA final formulas read with what I have? The attached document shows the formula.

I am not sure about my conclusion because I only address correlation.

Question for Class $2$: Use your MR model from class $1$ and add another MR model that is similar to the first. Combine the y variables and create two CFAs $($one endogenous from the y variables$),$ and a second CFA from the two MR independent variables list. Your answer will have two parts:

$1.$ Create two CFA models with six total variables $=$ three endogenous and three exogenous variables.

$2.$ Explain what you think the relationship might be between the CFA exogenous $($predictor concept$)$ upon the CFA endogenous concept $($conceptual outcome$).$

My response: Class $1$ MR Model: A model to assess an Operations Research System Analyst $($ORSA$)$ Productivity.

The dependent variable $($y$)=$ productivity score of ORSAs.

The independent variables are:

$$ x$1=$ years of experience

$$ x$2=$ training hours per year

$$ x$3=$ number of completed projects per year

$$ x$4=$ position $($lead$,$ supporting role$)$

The traditional MR model equation: y $=$ a$1$x$1+$ a$2$x$2+$ a$3$x$3+$ a$4$x$4+$ e

where $($a$1,$a$2,$a$3,$a$4)$ are the coefficients that represent the contribution of each independent variable to the productivity score.

The enhanced MR model with expanded error equation:

y $=$ a$1$x$1+$ a$2$x$2+$ a$3$x$3+$a$4$x$4+$ e$1($x$1)+$e$2($x$2)+$ e$3($x$3)+$ e$4($x$4)$

where $($e$1($x$1),$e$2($x$4),$e$3($x$3),$e$4($x$4))$ are the expanded error terms.

The most significant correlated errors might occur between:

$1.$ e$1$ and e$2$: Misaligned training for more experienced analysts.

$2.$ e$1$ and e$4$: If promotion is based on performance rather than experience.

$3.$ e$3$ and e$4$: Lead analyst with fewer projects to complete.

Below is a second MR model similar to the one from Class $1$:

A model to assess an Operations Research System Analyst $($ORSA$)$ Quality and Innovation.

The dependent variables $($y$)=$ quality and innovation scores of ORSAs.

The independent variables are:

$$ x$1=$ years of experience

$$ x$2=$ number of completed projects per year

$$ x$3=$ position $($lead$,$ supporting role$)$

CFA $1$ Exogenous Variables

$[$ORSA Characteristics$]$

V$1=$ years of experience $($x$1)$

V$2=$ number of completed projects per yr $($x$2)$

V$3=$ position $($lead$,$ supporting role$)($x$3)$

CFA $1$ represents the exogenous variables $($predictors$)$ that influence ORSA performance.

CFA $2$ Endogenous Variables

$[$ORSA Performance$]$

V$1=$ productivity score $($n$1)$

V$2=$ quality score $($n$2)$

V$3=$ innovation score $($n$3)$

CFA $2$ represents the endogenous variables $($outcomes$)$ influenced by the ORSA characteristics.

The interrelationships I may find and the factor loadings about how much of the exogenous variable$$s behavior is explained by the endogenous variable or$,$ in other words, how strongly each observed variable is connected or influenced by the unobserved variables are depicted below:

I will probably find x$1($years of experience$)$ closely related to productivity and quality. However, a slightly weaker relationship with innovation since more experience generally leads to higher productivity and often improves the ability to produce high$-$quality solutions. However, highly innovative approaches may require fresh perspectives. Thus, I would probably start the factor loadings with strong loadings of $0\mathrm{.}85$ for n$1($eta $1),0\mathrm{.}90$ for n$2($the quality score as the highest factor loading$),$ and $0\mathrm{.}75$ for n$3,$ respectively.

The x$2($number of completed projects$)$ may predict productivity and innovation since a high number of completed projects strongly correlates with productivity, which may also expose the ORSA to diverse issues that require solutions. x$2$ may not always correlate with quality since a higher number of projects may focus on quantity over quality, leading to burnout. x$2$ will primarily predict productivity and innovation but may slightly trade off with quality. I would probably start the strong factor loadings at $0\mathrm{.}95$ for n$1$ and $0\mathrm{.}85$ for n$3$ but moderately predict quality $($n$2)$ at $0\mathrm{.}70.$

The x$3($position$)$ will predict quality and innovation, less so productivity, as leadership roles are associated with higher responsibility and creativity but a weaker influence on productivity as lead positions involve more planning and coordination than actual task completion. x$3$ will moderately predict productivity $(0\mathrm{.}70)$ and strongly predict both quality $(0\mathrm{.}90)$ and innovation $(0\mathrm{.}90).$

In conclusion, I expect ORSA's years of experience to strongly influence and correlate all outcomes, especially quality, due to expected knowledge. The number of completed projects will primarily drive productivity and innovation but may slightly