# Predicted Probability Plots For Probit

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### Ugur Ozdemir

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Mar 29, 2020, 7:34:12 PM3/29/20
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Dear community,

I have two kind'a related questions and any help will be much appreciated.

1- As far as I understand, lavaan still does not have the logit link even if the help file states otherwise. Is this correct? So, probit is the only way to go if we have a binary outcome variable?

2- Let's say I have the following baby model with a binary outcome variable (vote) where I use a probit link. What would be the easiest way to plot the predicted probability plot for the latent variable, conf? (Predicted probabilities for different values of conf fixing all other variables.)
Note that conf is also in the mediated through migr

model <- '
# 1. measurement model
conf =~ k1 + k2
univ =~ k3 + k4

# outcome model
vote ~ c1*conf + c2*univ + b1*migr + age + gender

# mediator models
migr ~ a1*conf + a2*univ + age + gender

# indirect effects (IDE)
migrconf := b1*a1
migruniv := b1*a2

# total effects
totalConf := c1 + migrconf
totalConf := c2 + migruniv
'

### Nickname

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Mar 30, 2020, 10:29:39 AM3/30/20
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Ugur,
I believe your are correct about the logit link.  This is not something that I do every day, so hopefully I have not missed anything.  Here is a simple example.

summary(HolzingerSwineford1939)

# simplified mediation model
babyModel
<- '
school ~ x1 + x2
x1 ~ x2
school~~school
x1~~x1
school | t1
x1 ~ 1
'
# end babyModel

# Examine and Fit model
lavaanify
(babyModel)
babyFit
<- lavaan(babyModel, data=HolzingerSwineford1939, ordered=c('school'))
summary
(babyFit)

# Extract coefficients from model fit
babyCoef
<- coef(babyFit)
# Choose a set a values for the predictor
plotX2
<- seq(from=0, to=9, len=100)
# Predict mediator values
plotX1
<- babyCoef[6] + babyCoef[3]*plotX2
# Predict latent continuous outcome values
plotSchoolZ
<- babyCoef[1]*plotX1 + babyCoef[2]*plotX2
# predict probabilities
plotSchoolP
<- pnorm(plotSchoolZ)

# Draw plot
plot
(x=plotX2, y=plotSchoolP, type='l', lwd=2, xlab='Mediated Predictor',
ylab
='Predicted Probability of Outcome', main='Predicted Probability Plot')

Keith
------------------------
Keith A. Markus
John Jay College of Criminal Justice, CUNY
http://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.
http://www.routledge.com/books/details/9781841692203/

### Ugur Ozdemir

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Mar 30, 2020, 7:36:44 PM3/30/20
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Hi Keith,

Thank you very much for your response. It was tedious but I was able to do it, and your example code definitely helped.

Cheers,
Ugur
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