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On / By / With The building blocks of the Mplus language

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(regressed) On X1X1 Y1Y1 Outcome Y 1 is regressed ON covariate X 1

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(regressed) On X2X2 Y1Y1 X1X1 X3X3 Y2Y2 Y3Y3

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(measured) By Y1Y1 Y2Y2 Y4Y4 Y3Y3 F Latent, continuous factor F is measured BY the 4 continuous manifest variables Y 1 – Y 4

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(measured) By F by y1 – y4; Alternatively F by y1* y2 y3 y4; F@1;

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(correlated) With Factor F 1 is correlated with factor F 2 F1F1 F2F2

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By / With Y1Y1 Y2Y2 Y4Y4 Y3Y3 F1F1 Factor F 1 is measured by Y 1, Y 2 Factor F 2 is measured by Y 3, Y 4 Factors F 1 and F 2 are correlated F2F2

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By / With Y1Y1 Y2Y2 Y4Y4 Y3Y3 F1F1 Factor F 1 is measured by Y 1, Y 2 F2F2

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By / With Y1Y1 Y2Y2 Y4Y4 Y3Y3 F1F1 Factor F 1 is measured by Y 1, Y 2 Factor F 2 is measured by Y 3, Y 4 F2F2

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By / With Y1Y1 Y2Y2 Y4Y4 Y3Y3 F1F1 Factor F 1 is measured by Y 1, Y 2 Factor F 2 is measured by Y 3, Y 4 Factors F 1 and F 2 are correlated F2F2

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By / With F1 by y1 y2; F2 by y3 y4; F1 with F2; Or F1 by y1* y2; F2 by y3* y4; F1 with F2; F1@1 F2@0;

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Altogether now…. Y1Y1 Y2Y2 Y4Y4 Y3Y3 F1F1 F2F2 X1X1 X2X2 X3X3

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