The MCMC Procedure

Some Useful SAS Functions

Table 54.41 Some Useful SAS Functions
SAS Function	Definition
`abs(x)`	$\text{[math]}$
`airy(x)`	Returns the value of the AIRY function.
`beta(x1, x2)`	$\text{[math]}$
`call logistic(x)`	$\text{[math]}$
`call softmax(x1,...,xn)`	Each element is replaced by $\text{[math]}$
`call stdize(x1,...,xn)`	Standardize values
`cdf`	Cumulative distribution function
`cdf(’normal’, x, 0, 1)`	Standard normal cumulative distribution function
`comb(x1, x2)`	$\text{[math]}$
`constant(’.’)`	Calculate commonly used constants
`cos(x)`	cosine(x)
`css(x1, ..., xn)`	$\text{[math]}$
`cv(x1, ..., xn)`	std(x) / mean(x) * 100
`dairy(x)`	Derivative of the AIRY function
`dimN(m)`	Returns the numbers of elements in the Nth dim of array $\text{[math]}$
`(x1 eq x2)`	Returns 1 if x1 = x2; 0 otherwise
`x1x2`**	$\text{[math]}$
`geomean(x1, ..., xn)`	$\text{[math]}$
`difN(x)`	Returns differences between the argument and its Nth lag
`digamma(x1)`	$\text{[math]}$
`erf(x)`	$\text{[math]}$
`erfc(x)`	1 - erf(x)
`fact(x)`	$\text{[math]}$
`floor(x)`	Greatest integer $\text{[math]}$
`gamma(x)`	$\text{[math]}$
`harmean(x1, ..., xn)`	$\text{[math]}$
`ibessel(nu, x, kode)`	Modified Bessel function of order nu evaluated at $\text{[math]}$
`jbessel(nu, x)`	Bessel function of order nu evaluated at $\text{[math]}$
`lagN(x)`	Returns values from a queue
`largest(k, x1, ..., xn)`	Returns the $\text{[math]}$ largest element
`lgamma(x)`	$\text{[math]}$
`lgamma(x+1)`	$\text{[math]}$
`log(x), logN(x)`	$\text{[math]}$
`logbeta(x1, x2)`	lgamma( $\text{[math]}$ ) + lgamma( $\text{[math]}$ ) - lgamma( $\text{[math]}$ )
`logcdf`	Log of a left cumulative distribution function
`logpdf`	Log of a probability density (mass) function
`logsdf`	Log of a survival function
`max(x1, x2)`	Returns $\text{[math]}$ if $\text{[math]}$ ; $\text{[math]}$ otherwise
`mean(of x1-xn)`	$\text{[math]}$
`median(of x1-xn)`	Returns the median of nonmissing values
`min(x1, x2)`	Returns $\text{[math]}$ if $\text{[math]}$ ; $\text{[math]}$ otherwise
`missing(x)`	Returns 1 if $\text{[math]}$ is missing; 0 otherwise
`mod(x1, x2)`	Returns the remainder from $\text{[math]}$
`n(x1, ..., xn)`	Returns number of nonmissing values
`nmiss(of y1-yn)`	Number of missing values
`quantile`	Computes the quantile from a specific distribution
`pdf`	Probability density (mass) functions
`perm(n, r)`	$\text{[math]}$
`put`	Returns a value that uses a specified format
`round(x)`	Rounds x
`rms(of x1-xn)`	$\text{[math]}$
`sdf`	Survival function
`sign(x)`	Returns $\text{[math]}$ if $\text{[math]}$ ; $\text{[math]}$ if $\text{[math]}$ ; $\text{[math]}$ if $\text{[math]}$
`sin(x)`	sine( $\text{[math]}$ )
`smallest(, x1, ..., en )`	Returns the $\text{[math]}$ smallest component of $\text{[math]}$
`sortn(of x1-xn)`	Sorts the values of the variables
`sqrt(x)`	$\text{[math]}$
`std(x1, ..., xn)`	Standard deviation of $\text{[math]}$ (n-1 in denominator)
`sum(of x:)`	$\text{[math]}$
`trigamma(x)`	Derivative of the DIGAMMA( $\text{[math]}$ ) function
`uss(of x1-xn)`	Uncorrected sum of squares

Here are examples of some commonly used transformations:

logit

mu = beta0 + beta1 * z1;
call logistic(mu);

log
```
w = beta0 + beta1 * z1;
mu = exp(w);
```

probit

w = beta0 + beta1 * z1;
mu = cdf(`normal', w, 0, 1);

cloglog

w = beta0 + beta1 * z1;
mu = 1 - exp(-exp(w));