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| Create Spline from Coefficients and Knots [ Reply ] By: L Bogaardt on 2019-12-20 11:18 | [forum:47292] 28Kyb.png (0) downloads
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In GAMLSS, it is possible to model a random variable $Y$ as a smoothed non-parametric function of some predictor $x$. One option for such a function is the penalised spline using `y~pb(x)`. This outputs a list of coefficients and knots which, combined with a set of basis splines, results in a smooth function of $x$. How can one recreate the spline function, given the coefficients and the knots? (and without having to write my own b-spline generating function). For example: library(gamlss) set.seed(9876) xstart <- 0 xend <- 100 datan <- 20000 seq <- seq(xstart, xend) mean <- sapply(seq, function(x){0.5+0.2*sin(x/10)}) xs <- ceiling(runif(datan, xstart, xend)) ys <- sapply(xs, function(x){rnorm(1, mean = mean[x], sd = 0.1)}) m1 <- gamlss(ys~pb(xs)) plot(xs, ys) lines(seq, mean, col="red") lines(xs[order(xs)], fitted(m1)[order(xs)], col="green") intercept <- m1$mu.coefficients[1] # 0.5495853 weight <- m1$mu.coefficients[2] # -0.0002851018 coefficients <- c(m1$mu.coefSmo[[1]]$coef) # c(-0.170704842, -0.066451626, 0.026591530, 0.119289203, 0.159657021, 0.149185418, 0.086505094, 0.003904402, -0.100156999, -0.188811997, -0.238717366, -0.237884900, -0.197802945, -0.090559794, 0.012576273, 0.101003289, 0.169210741, 0.181836117, 0.143883546, 0.061281663, -0.038608572, -0.136215586, -0.232871483) knots <- m1$mu.coefSmo[[1]]$knots # c(-5.039, 0.010, 5.059, 10.108, 15.157, 20.206, 25.255, 30.304, 35.353, 40.402, 45.451, 50.500, 55.549, 60.598, 65.647, 70.696, 75.745, 80.794, 85.843, 90.892, 95.941 100.990 106.039) How can I obtain the green function, knowing only the intercept, weight, coefficients and knots? I currently plot this function using `fitted(m1)`. However, this is simply a list of $y$ values for the originally inputted list of $x$ values, it is not a function which gives $y$ for any new $x$. |
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