Adding quadratic term decreases goodness-of-fit

[모르모트군]

Hello,

I'd like to test the quadric effects of z1 on y, in my path model, so I added the squared term.

data$z1.square <- (data$z1)^2

path1.square <-
  'x1~ A1*v1+
c1*a1+c2*a2+ c3*a3+c4*a4+c5*a5

x2~ A2*v1+
c11*a1+c12*a2+c13*â3+c14*a4+c15*a5

z1~ C1*x1+D1*x2
+G1*a1+  c21*a2+c22*a3+c23*a4+c24*a5


y~H1*z1+H2*v1+H3*z1.square+
d1*x1+d2*x2+
c61*a1+c62*a2+c63*a3+c64*a4+c65*a5

x1 ~~ x2
'#without square terms

Test statistics look fine here; chisquare = 2.520, df=1, p-value is 0.07.

Then I just simply add the quadratic term of z1

path1 <-
  'x1~ A1*v1+
c1*a1+c2*a2+ c3*a3+c4*a4+c5*a5

x2~ A2*v1+
c11*a1+c12*a2+c13*â3+c14*a4+c15*a5

z1~ C1*x1+D1*x2
+G1*a1+  c21*a2+c22*a3+c23*a4+c24*a5


y~H1*z1+H2*v1+
d1*x1+d2*x2+
c61*a1+c62*a2+c63*a3+c64*a4+c65*a5

x1 ~~ x2
'#without square terms

Then suddenly the model becomes insignificant.

chisquare= 1840.910, df= 6, p-value is 0.00

Also, TLI goes to minus. 

To my knowledge, adding the quadratic term should increase the goodness of fit. Why does this happen?

[Christian Arnold]

I suspect you are confusing R^2 with model fit (chi square, fit indices). Here is a good starting Point: https://www.researchgate.net/publication/263085914_Testing_Multiple_Nonlinear_Effects_in_Structural_Equation_Modeling_A_Comparison_of_Alternative_Estimation_Approaches

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Von: lav...@googlegroups.com <lav...@googlegroups.com> im Auftrag von 모르모트군 <bark...@gmail.com>
Gesendet: Donnerstag, 29. September 2022, 20:59
An: lavaan <lav...@googlegroups.com>
Betreff: Adding quadratic term decreases goodness-of-fit

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