I have some observations $y$ which have only few negative values $y_i\in (-\infty,0)$ and mostly non-negativ values, i.e. $y_i\in [0,\infty)$. I would like to estimate a censored logistic distribution depending on some variables x1, x2 for y with GAMLSS. Therefore I assume that the y is left-censored at zero (as nearly all values are non-negativ). However, I am not sure, if I specified the formula part with the survival object for this model correctly in GAMLSS. I used the following R-code

    # generates left censored logistic distribution called "LOlc"    
    gen.cens(family = "LO", type = "left")  
    # estimate model
    model <-  gamlss(formula = Surv(y, y >= 0, type = "left") ~ x1 + x2, 
                     sigma.formula = ~ x1 + x2, 
                     nu.formula = ~ 1,
                     tau.formula = ~ 1,
                     family = "LOlc", # 
                     data = na.omit(data))

Could you tell me, if I specified Surv(y, y >= 0, type = "left") in the formula argument correctly and if I generated the correct distribution for my assumption with gen.cens for this situation? Thank you!



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