Error in model.frame.default: variable lengths differ

Joran suggested to first remove the NAs before running the model. Thus, I removed the NAs, run the model and obtained the residuals. When I updated model2 by inclusion of the lagged residuals, the error message did not appear again.

Remove NAs

df2<-df1[complete.cases(df1),]

Run the main model

model2<-gam(death ~ pm10 + s(trend,k=14*7)+ s(temp,k=5), data=df2, family=poisson)

Obtain residuals

resid2 <- residuals(model2,type="deviance")

Update model2 by including the lag 1 residuals

model2_1 <- update(model2,.~.+ Lag(resid2,1),  na.action=na.omit)

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