# lower_bd: lower bound of expit(x) In zhenkewu/lotR: Latent class analysis with Observed Trees in R (lotR)

 lower_bd R Documentation

## lower bound of expit(x)

### Description

lower bound is quadratic in the exponent

### Usage

```lower_bd(xi)
```

### Arguments

 `xi` local variational parameter, positive value, this is where the `expit(xi) = lower_bd(xi)`; this is where the quadratic and expit curve contact

### Value

a positive value between `0` and `1`

### References

Other VI functions: `approx_sb()`, `g_fun.vec()`, `g_fun0()`, `g_fun()`

### Examples

```
par(mfrow=c(2,3))
xi_seq <- c(0.1,0.5,1,2,4,6)
x <- seq(-5,5,by=0.1)
for (i in 1:length(xi_seq)){
xi <- xi_seq[i]
y1 <- lower_bd(xi)(x)
y2 <- lower_bd(-xi)(x)

plot(x,y1,type="l",col="red",ylim=c(0,1),main=paste0("xi= ",xi))
points(x,y2,type="l",col="blue")
points(x,1/(1+exp(-x)),type="l",col="orange")
abline(v=c(-xi,xi),col="gray")
legend("topleft",c("expit","bound"),col=c("orange","blue"),lty=c(1,1))
}

```

zhenkewu/lotR documentation built on April 24, 2022, 2:36 a.m.