Unusual residual plot of mixed effects model fitted with lme in R (zero-inflated DV?)

Question

I ran a mixed effect model in R by using lme() to analyze the following data (an excerpt is shown in the following):

   name   day daily_amount lag_raised_amount inv_count length
  <chr> <dbl>        <dbl>             <dbl>     <dbl>  <dbl>
1 abcde     2          232              1901        20     58
2 abcde     3         1023              2133        23     58
3 abcde     4          101              3156        24     58
4 abcde     5            0              3257        24     58
5 abcde     6            0              3257        24     58
6 abcde     7         4500              3257        24     58

In sum I have an unbalanced panel with the following metrics

$n=name=131, T=day=8-102, N=6680$

Background of the data set: I observed funding campaigns of companies on a daily basis. In a first step I want to measure some kind of "herding", specifically whether the daily_amount raised on day $t$ depends on the total lag_raised_amount observed on day $t-1$ (plus controlled for various company-sepcific fixed effects such as (campaign)length and time-varying effects such as investor count).

I ran the following (here abbreviated) model to account for this structure and auto-correlation:

mixed <- lme(log(daily_amount+1) ~ lag_raised_amount_log + I(lag_raised_amount_log^2)
             + log(lag_inv_count+1) + I(log(lag_inv_count^2+1)) + log(length) 
             + day + I(day^2) 
             , random = list(~day|name), data = panel, correlation = corAR1())

Assessing the the fit of this model gives me now a headache for some time:

The QQ-Plot and the binned residuals as suggested by Gelman and Hill (2007) look fine.

The normal residuals plot, however, looks a bit weird to me: it is somewhat turned by 45 degrees and the straight "line" looks off.

I suspect that this may be due to the fact that ~48% of my DV are zeros, but after trying for days I have honestly no clue what to do about.

My questions:

1. Is the residual plot as alarming as I think?
2. What can I do about it, specifically, how can I better account for the zero-inflated DV? I know quite a bit about modelling zero-inflated continuous DVs with hurdle models, but I haven't found anything comparable in context of mixed effects models (+ I am not sure whether this is necessary at all).

Answer 1

1. In my opinion yes, this doesn't look ideal.

2. http://glmmadmb.r-forge.r-project.org allows specifying constant zero-inflated GLMMs with a range of distribution, including the negative binomial, which would be a candidate here. However, afaik, you can't specify the AR1 temporal structure with this function. The only way I am aware to specify zero-inflation, arbitrary distributions and temporal structure at the same time is using directly one of the general modeling environments, such as Jags, STAN, or ADMB. Before going there, however, I would probably fit the glmmadmb first and check if there is temporal correlation in the first place.