You could use a likelihood ratio test but to decide with distribution to choose, you should do some model validation steps first, i.e. checking residuals for any patterns that would indicate the distributional fit is appropriate (or not) as well as checking your models for overdispersion.

Model comparisons as you performed via the Likelihood ratio test are more common to decide which fixed effect combinations can explain the data best. The output of the test suggests that your second model (negative binomial) explains the data better and hence is a significantly better fit (as indicated by the p-value).

There are quite a few answers on model selection over at https://stats.stackexchange.com/, e.g. https://stats.stackexchange.com/a/325431/32477

Also check the documentation for the countreg R package here: https://cran.r-project.org/web/packages/pscl/vignettes/countreg.pdf as well as for rootograms: https://arxiv.org/pdf/1605.01311.pdf

You could use a likelihood ratio test but to decide with distribution to choose, you should do some model validation steps first, i.e. checking residuals for any patterns that would indicate the distributional fit is appropriate (or not) as well as checking your models for overdispersion.

Model comparisons as you performed via the Likelihood ratio test are more common to decide which fixed effect combinations can explain the data best. The output of the test suggests that your second model (negative binomial) explains the data better and hence is a significantly better fit (as indicated by the p-value).

Check the documentation for the countreg R package here: https://cran.r-project.org/web/packages/pscl/vignettes/countreg.pdf as well as for rootograms: https://arxiv.org/pdf/1605.01311.pdf

Also there are also quite a few answers on model selection and Poisson/negative binomial here on Cross Validated, e.g. https://stats.stackexchange.com/a/325431/32477

You could use a likelihood ratio test but to decide with distribution to choose, you should do some model validation steps first, i.e. checking residuals for any patterns that would indicate the distributional fit is appropriate (or not) as well as checking your models for overdispersion.

Model comparisons as you performed via the Likelihood ratio test are more common to decide which fixed effect combinations can explain the data best. The output of the test suggests that your second model (negative binomial) explains the data better and hence is a significantly better fit (as indicated by the p-value).

There are quite a few answers on model selection over at https://stats.stackexchange.com/, e.g. https://stats.stackexchange.com/a/325431/32477

You could use a likelihood ratio test but to decide with distribution to choose, you should do some model validation steps first, i.e. checking residuals for any patterns that would indicate the distributional fit is appropriate (or not) as well as checking your models for overdispersion.

Model comparisons as you performed via the Likelihood ratio test are more common to decide which fixed effect combinations can explain the data best. The output of the test suggests that your second model (negative binomial) explains the data better and hence is a significantly better fit (as indicated by the p-value).

There are quite a few answers on model selection over at https://stats.stackexchange.com/, e.g. https://stats.stackexchange.com/a/325431/32477

Also check the documentation for the countreg R package here: https://cran.r-project.org/web/packages/pscl/vignettes/countreg.pdf as well as for rootograms: https://arxiv.org/pdf/1605.01311.pdf