Find the likelihood-based confidence bound for one parameter.

## Arguments

- i
The position (row number) of the target parameters as appeared in the parameter table of the lavaan::lavaan object.

- which
Whether the lower bound or the upper bound is to be found. Must be

`"lbound"`

or`"ubound"`

.- sem_out
The SEM output. Currently supports lavaan::lavaan outputs only.

- method
The approach to be used. Default is

`"wn"`

(Wu-Neale-2012 Method). Another method is "ur", root finding by`stats::uniroot()`

.- standardized
Logical. Whether the bound of the LBCI of the standardized solution is to be searched. Default is

`FALSE`

.- robust
Whether the LBCI based on robust likelihood ratio test is to be found. Only

`"satorra.2000"`

in`lavaan::lavTestLRT()`

is supported for now. If`"none"`

, the default, then likelihood ratio test based on maximum likelihood estimation will be used. For "ur",`"satorra.2000"`

is automatically used if a scaled test statistic is requested in`sem_out`

.- sf_full
A list with the scaling and shift factors. Ignored if

`robust`

is`"none"`

. If`robust`

is`"satorra.2000"`

and`sf_full`

is supplied, then its value will be used. If`robust`

is`"satorra.2000"`

but`sf_full`

is`NA`

, then scaling factors will be computed internally.- sf_args
The list of arguments to be used for computing scaling factors if

`robust`

is`"satorra.2000"`

. Used only by`semlbci()`

. Ignored if`robust`

is not`"satorra.2000"`

.- sem_out_name
The name of the object supplied to

`sem_out`

.`NULL`

by default. Originally used by some internal functions. No longer used in the current version but kept for backward compatibility.- try_k_more_times
How many more times to try if the status code is not zero. Default is 0.

- ...
Arguments to be passed to the function corresponds to the requested method (

`ci_bound_wn_i()`

for "wn").

## Value

A list of the following elements.

`bound`

: The bound located.`NA`

if the search failed.`diags`

: Diagnostic information.`method`

: Method used. Currently only`"wn"`

is the only possible value.`times`

: Total time used in the search.`sf_full`

: The scaling and shift factors used.`ci_bound_i_out`

: The original output from`ci_bound_wn_i()`

.`attempt_lb_var`

: How many attempts used to reduce the lower bounds of free variances.`attempt_more_times`

: How many additional attempts used to search for the bounds. Controlled by`try_k_more_times`

.

## Details

### Important Notice

This function is not supposed to be used directly by users in
typical scenarios. Its interface is user-*unfriendly* because it
should be used through `semlbci()`

. It is exported such that
interested users can examine how a confidence bound is found, or
use it for experiments or simulations.

### Usage

`ci_i_one()`

is the link between `semlbci()`

and the lowest level
function (currently `ci_bound_wn_i()`

). When called by `semlbci()`

to find the bound of a parameter, `ci_i_one()`

calls a function
(`ci_bound_wn_i()`

by default) one or more times to find the bound
(limit) for a likelihood-based confidence interval.

## Examples

```
data(simple_med)
library(lavaan)
mod <-
"
m ~ x
y ~ m
"
fit_med <- lavaan::sem(mod, simple_med, fixed.x = FALSE)
parameterTable(fit_med)
#> id lhs op rhs user block group free ustart exo label plabel start est
#> 1 1 m ~ x 1 1 1 1 NA 0 .p1. 1.676 1.676
#> 2 2 y ~ m 1 1 1 2 NA 0 .p2. 0.535 0.535
#> 3 3 m ~~ m 0 1 1 3 NA 0 .p3. 34.710 34.710
#> 4 4 y ~~ y 0 1 1 4 NA 0 .p4. 40.119 40.119
#> 5 5 x ~~ x 0 1 1 5 NA 0 .p5. 0.935 0.935
#> se
#> 1 0.431
#> 2 0.073
#> 3 3.471
#> 4 4.012
#> 5 0.094
# Find the LBCI for the first parameter
# The method "wn" needs the constraint function.
# Use set_constraint() to generate this function:
fn_constr0 <- set_constraint(fit_med)
# Call ci_i to find the bound, the lower bound in this example.
# The constraint function, assigned to f_constr, is passed
# to ci_bound_wn_i().
# npar is an argument for ci_bound_wn_i().
out <- ci_i_one(i = 1,
which = "lbound",
sem_out = fit_med,
npar = 5,
f_constr = fn_constr0)
out$bounds
#> lbound
#> 0.827702
```