yield ~ mu variety mv !r blocks
| Reserved model terms | ||
| mu | constant term or intercept | fixed |
| mv | a term to estimate missing values | fixed |
| Trait | multivariate counterpart to mu | fixed |
| units | forms a factor with a level for each experimental unit | random |
| Operators | ||
| : | placed between labels to specify an interaction | both |
| / | forms nested expansion | both |
| * | forms factorial expansion | fixed |
| - | placed before model terms to exclude them from the model | both |
|
, | at the end of a line indicates the model specification continues on the next line | both |
| - | treated as a space | both |
| !{ ... !} | placed around some model terms when it is important the terms not be reordered | random |
| Common functions | ||
| at(f,n) | condition on level n of factor f. n may be a list of values | both |
| at(f) | forms conditioning covariables for all levels of factor f | both |
| fac(v) | forms a factor from v with a level for each unique value in v | both |
| fac(v,y) | forms a factor with a level for each combination of values in v and y | random |
| lin(f) | forms a variable from the factor f with values equal to 1... n corresponding to level(1) ... level( n) of the factor | both |
|
spl(v)
spl(v,k) | forms the design matrix for the random component of a cubic spline for variable v | random |
| other functions | ||
|
and(t)
and(t,r) | adds r times the design matrix for model term t to the previous design matrix; r has a default value of 1. | both |
|
c(f)
con(f) | factor f is fitted with sum to zero constraints | fixed |
| cos(v,r) | forms cosine from v with period r | fixed |
| ge(f,r) | condition on factor/variable f >= r | fixed |
| giv(f,n) | associates the nth .giv G-inverse with the factor f | random |
| gt(f,r) | condition on factor/variable f > r | fixed |
| h(f) | factor f is fitted with Helmert constraints | fixed |
| ide(f) | fits pedigree factor f without relationship matrix | random |
|
inv(v)
inv(v,r) | forms reciprocal of v + r | fixed |
| le(f,r) | condition on factor/variable f <= r | fixed |
| leg(v,[-]n) | forms n+1 legendre polynomials of order 0 (intercept), 1 (linear) ... n from the values in v; the intercept polynomial is omitted if v is preceded by the negative sign. | fixed |
| lt(f,r) | condition on factor/variable f < r | fixed |
| log(v[,r]) | forms natural logarithm of v + r | fixed |
| ma1(f) | constructs MA1 design matrix for factor f | random |
| ma1 | forms an MA1 design matrix from plot numbers | random |
| out(n) | condition on observation n | fixed |
| out(n,t) | condition on record n, trait t | fixed |
| pol(v,[-]n) | forms n+1 orthogonal polynomials of order 0 (intercept), 1 (linear) ... n from the values in v; the intercept polynomial is omitted if n is preceded by the negative sign. | both |
| pow(v,p[,r]) | raises v + r to power p | fixed |
| qtl(f,r) | impute a covariable from marker map information at position r | fixed |
| sin(v,r) | forms sine from v with period r | both |
| sqrt(f[,r]) | forms square root of v + r | fixed |
| uni(f) | forms a factor with a level for each record where factor f is non-zero | random |
| uni(f,n) | forms a factor with a level for each record where factor f has level n | random |
| xfa(f,k) | is formally a copy of factor f with k extra levels. This is used when fitting extended factor analytic models ( XFA, of order k. | random |