VGAM (version 1.0-4)

s: Defining Smooths in VGAM Formulas


s is used in the definition of (vector) smooth terms within vgam formulas. This corresponds to 1st-generation VGAMs that use backfitting for their estimation. The effective degrees of freedom is prespecified.


s(x, df = 4, spar = 0, ...)



covariate (abscissae) to be smoothed. Note that x must be a single variable and not a function of a variable. For example, s(x) is fine but s(log(x)) will fail. In this case, let logx <- log(x) (in the data frame), say, and then use s(logx). At this stage bivariate smoothers (x would be a two-column matrix) are not implemented.


numerical vector of length \(r\). Effective degrees of freedom: must lie between 1 (linear fit) and \(n\) (interpolation). Thus one could say that df-1 is the effective nonlinear degrees of freedom (ENDF) of the smooth. Recycling of values will be used if df is not of length \(r\). If spar is positive then this argument is ignored. Thus s() means that the effective degrees of freedom is prespecified. If it is known that the component function(s) are more wiggly than usual then try increasing the value of this argument.


numerical vector of length \(r\). Positive smoothing parameters (after scaling) . Larger values mean more smoothing so that the solution approaches a linear fit for that component function. A zero value means that df is used. Recycling of values will be used if spar is not of length \(r\).

Ignored for now.


A vector with attributes that are (only) used by vgam.


In this help file \(M\) is the number of additive predictors and \(r\) is the number of component functions to be estimated (so that \(r\) is an element from the set {1,2,…,\(M\)}). Also, if \(n\) is the number of distinct abscissae, then s will fail if \(n < 7\).

s, which is symbolic and does not perform any smoothing itself, only handles a single covariate. Note that s works in vgam only. It has no effect in vglm (actually, it is similar to the identity function I so that s(x2) is the same as x2 in the LM model matrix). It differs from the s() of the gam package and the s of the mgcv package; they should not be mixed together. Also, terms involving s should be simple additive terms, and not involving interactions and nesting etc. For example, myfactor:s(x2) is not a good idea.


Yee, T. W. and Wild, C. J. (1996) Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481--493.

See Also

vgam, is.buggy, sm.os,, vsmooth.spline.


Run this code
# Nonparametric logistic regression
fit1 <- vgam(agaaus ~ s(altitude, df = 2), binomialff, data = hunua)
# }
 plot(fit1, se = TRUE) 
# }
# Bivariate logistic model with artificial data
nn <- 300
bdata <- data.frame(x1 = runif(nn), x2 = runif(nn))
bdata <- transform(bdata,
    y1 = rbinom(nn, size = 1, prob = logit(sin(2 * x2), inverse = TRUE)),
    y2 = rbinom(nn, size = 1, prob = logit(sin(2 * x2), inverse = TRUE)))
fit2 <- vgam(cbind(y1, y2) ~ x1 + s(x2, 3), trace = TRUE,
             binom2.or(exchangeable = TRUE), data = bdata)
coef(fit2, matrix = TRUE)  # Hard to interpret
# }
 plot(fit2, se = TRUE, which.term = 2, scol = "blue") 
# }

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