1 a latent variable model. 2 grace keeley 2006 ecol apps example: observed variable model

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1 A Latent Variable Model

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3 How do we create a latent variable? (1) First, use this tool to draw an ellipse, representing a latent variable. (2) To name it, right click on the ellipse, select “object properties”, and name it “Land”.

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Page 1: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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A Latent Variable Model

Page 2: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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Grace & Keeley 2006 Ecol Apps Example: Observed Variable Model

Page 3: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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How do we create a latent variable?

(1) First, use this tool to draw an ellipse, representing a latent variable. (2) To name it, right click on the ellipse, select “object properties”, and name it “Land”.

Page 4: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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How do we create a latent variable? (cont.)

(3) Select this tool and click it on Land once to create a single indicator.

(4) You can open and drag from the list of variables the variable coastran, which is our indicator for Land.(5) Remember, you still need to

name the error for coastran!

default weight from latent to indicator is set at 1 for single indicator.

path from error to indicator set to 1.

Page 5: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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How do we create a latent variable? (cont.)

(6) Keep in mind that if a latent variable is endogenous, it will need its own error variable (Le1 in this case).

Page 6: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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Grace & Keeley 2006 Example with Latent Variables

We are now modeling interactionsamong latent variables.

Each LV has an indicator andeach indicator has an error.

Endogenous LVs haveprediction errors.

Indicator errors have beenset to zero (i.e., there isno measurement error).

Page 7: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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Grace & Keeley 2006 Example w/ LVs - Results

Results are identical to thosefrom the observed variablemodel.

Page 8: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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Grace & Keeley 2006 Example with Measurement Error

Measurement errorspecified in raw units.

Page 9: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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Grace & Keeley 2006 Example with ME - Results

Page 10: 1 A Latent Variable Model. 2 Grace  Keeley 2006 Ecol Apps Example: Observed Variable Model

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Comparison of Results

Can you find the main differences?