# Using k to Estimate and Test Patterns in the APIM David A. Kenny February 17, 2013.

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Using k to Estimate and Test Patterns in the APIM David A. Kenny February 17, 2013

You need to know the Actor Partner Interdependence Model and APIM patterns! 2 APIM APIM Patterns

Couple Model – Equal Actor and Partner Effects: a = p Contrast Model –Actor plus partner sums to zero: a – p = 0 Actor Only Model –Partner effect is zero: p = 0 Partner Only Model –Actor effect is zero: a = 0 3

Suggested by Kenny and Ledermann (2010) k is the ratio of the partner effect to the actor effect or p/a k is named after Larry Kurdek, a pioneer in the study of dyadic data Special cases of k: –k is 1, couple model –k equal to −1, contrast model –k equal to zero, actor-only model The Parameter k 4

-1 0 +1 Contrast Actor Only Couple a = -p p = 0 a = p 5

-1 0 +1 Contrast Actor Only Couple a = -p p = 0 a = p But k might equal 0.5. 6

Phantom Variables One way to estimate k is using a phantom variable. Phantom variable –No conceptual meaning –Forces a constraint –Latent variable –No disturbance 7

Standard APIM X1X1 X2X2 Y1Y1 Y2Y2 E1 E2 1 1 a1a1 p 21 p 12 a2a2 8

Phantom Variables to Estimate k X1X1 X2X2 Y1Y1 Y2Y2 E1 E2 1 1 a1a1 a2a2 P1P1 a1a1 k1k1 P2P2 a2a2 k2k2 9

Estimates and Confidence Interval Use bootstrapping to obtain the asymmetric confidence interval (CI). Check to see if 1, -1, or 0 are in the CI of k. 10

Note that k is not defined when the actor effect is zero. Thus, k and its confidence interval should not be computed if the actor effect is small. Caution in Computing the Parameter k

Distinguishability and k 12

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Results Distinguishable Wives: k W = 0.851 (0.223 to 2.038 ) Husbands: k H = 0.616 (0.294 to 1.187) Equal values of k k W = k H = 0.710 (0.489 to 0.989 )  2 (1) = 0.320, p =.571 Indistinguishable: k = 0.719 (0.484 to 1.027) 14 CI

Example Setups Amos and Mplus (and soon laavan) setups can be downloaded at davidakenny.net/papers/k_apim/k_apim.htm 15

Defining k in Terms of X or k X 16

X1X1 X2X2 Y1Y1 Y2Y2 E1 E2 1 1 a1a1 p 21 p 12 a2a2 17

X1X1 X2X2 Y1Y1 Y2Y2 E1 E2 1 1 a1a1 p 21 p 12 a2a2 18

Defining k in as Actor Effect Divided by Partner Effect 19

Conclusion Using k can simplify the model and link the model to theory. Reading Kenny & Ledermann (2010), Journal of Family Psychology, 24, pp. 359-366. 20

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