# quadratic effects

    library(modsem)

# Quadratic Effects and Interaction Effects

Quadratic effects are essentially a special case of interaction effects—where a variable interacts with itself. As such, all of the methods in `modsem` can also be used to estimate quadratic effects.

Below is a simple example using the `LMS` approach.

    library(modsem)
    m1 <- '
    # Outer Model
    X =~ x1 + x2 + x3
    Y =~ y1 + y2 + y3
    Z =~ z1 + z2 + z3

    # Inner model
    Y ~ X + Z + Z:X + X:X
    '

    est1Lms <- modsem(m1, data = oneInt, method = "lms")
    summary(est1Lms)

In this example, we have a simple model with two quadratic effects and one interaction effect. We estimate the model using both the `QML` and double-centering approaches, with data from a subset of the PISA 2006 dataset.

    m2 <- '
    ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5
    CAREER =~ career1 + career2 + career3 + career4
    SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6
    CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC
    '

    est2Dblcent <- modsem(m2, data = jordan)
    est2Qml <- modsem(m2, data = jordan, method = "qml")
    summary(est2Qml)

Note: The other approaches (e.g., `LMS` and constrained methods) can also be used but may be slower depending on the number of interaction effects, especially for the `LMS` and constrained approaches.