nonlinear regression in R with multiple data sets -

i learning r , using non linear regression (which learning). have 2 sets of data (duration of operation on different machines) , able find non linear regression each of these sets. now, find best regression minimise sum of both residual sum-of-squares.

here have :

a <- c(1:5) b <- c(100, 51, 32, 24, 19) c <- c(150, 80, 58, 39, 29)  df <- data.frame (a,b,c)  f <- b ~ k1/a + k2 g <- c ~ k1/a + k2  n <- nls(f, data = df, start = list(k1=10, k2=10)) p <- nls(g, data = df, start = list(k1=10, k2=10)) n #nonlinear regression model #  model: b ~ k1/a + k2 #   data: df #     k1      k2  #101.595  -1.195  # residual sum-of-squares: 2.619  #number of iterations convergence: 1  #achieved convergence tolerance: 2.568e-07  p #nonlinear regression model #  model: c ~ k1/a + k2 #   data: df #     k1      k2  #148.044   3.593  # residual sum-of-squares: 54.19  #number of iterations convergence: 1  #achieved convergence tolerance: 1.803e-07 

k1 , k2 constant (of course) different both sets (b , c), wondering how manage find particular k1 , particular k2 produce 'best' solution both data sets.

hope explanation understandable. otherwise, i'm trying find (at least here) called global non linear regression.

edit : know how can tell r avoid negative values specific parameter. in case, k2 positive.

if want identical parameters, should pool data:

df2 <- data.frame(y=c(df$b,df$c), x=rep(df$a, 2)) p <- nls(y ~ k1/x + k2,           data = df2,           start = list(k1=10, k2=10),           lower = c(0, 0),           algorithm = "port") summary(p)  #  formula: y ~ k1/x + k2 #   #  parameters: #    estimate std. error t value pr(>|t|)     #  k1  124.819     18.078   6.904 0.000124 *** #    k2    1.199      9.781   0.123 0.905439     #  --- #    signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #   #  residual standard error: 16.59 on 8 degrees of freedom #   #  algorithm "port", convergence message: both x-convergence , relative convergence (5) 

edit:

if want 1 parameter equal , 1 vary, use mixed effects model. however, don't know how specify constraints (i believe not simple task, possibly achieved reparameterization).

library(nlme)  library(reshape2) df3 <- melt(df, id.vars="a")  r <- nlme(value ~ k1/a + k2,            data = df3,            start = c(k1=10, k2=10),            fixed = k1 + k2 ~1,           random = k2 ~ 1|variable)  summary(r) #  nonlinear mixed-effects model fit maximum likelihood #  model: value ~ k1/a + k2  #  data: df3  #  aic      bic    loglik #  83.11052 84.32086 -37.55526 #   #  random effects: #    formula: k2 ~ 1 | variable #                k2 residual #  stddev: 12.49915 7.991013 #   #  fixed effects: k1 + k2 ~ 1  #         value std.error df   t-value p-value #  k1 124.81916  9.737738  7 12.818086  0.0000 #  k2   1.19925 11.198211  7  0.107093  0.9177 #  correlation:  #         k1     #  k2 -0.397 #   #  standardized within-group residuals: #    min         q1        med         q3        max  #  -1.7520706 -0.5273469  0.2746039  0.5235343  1.4971808  #   #  number of observations: 10 #  number of groups: 2   coef(r) #          k1        k2 #  b 124.8192 -10.81835 #  c 124.8192  13.21684