How to design DESeq2 LRT model with individuals nested in 2 levels?
From what I can gather, you want to account for the effect of individual, nested within region. That is, you want to see after accounting for these, is there a consistent effect for Injection:Social across all conditions.
So you set up the model like this:
m1 &lt;- model.matrix(~ ind.n*Region + Injection + Social + Injection:Social,data=..)

The last term should be Injection:Region and you can just use the waldTest (default) in DESeq2 for this term.
What does the terms do? ind.n*Region is the equivalent of ind.n + Region + ind.n:Region , and with this you effectively get an effect for every region in every individual.
Why don't we need the Injection:ind.n or Social:ind.n or Social:Region. These terms indicate the effect of Injection or Social can vary by individuals or regions. Most likely introducing too many parameters when you are interested in a common effect. Also you do not have the replicates or samples to distinguish this effect from region or other effects.
Since you provided an example we can run DESeq2 and you can see how the results look like:
mat = counts(makeExampleDESeqDataSet(n=1000,m=48))
dds = DESeqDataSetFromMatrix(mat,df,~ ind.n*Region + Injection + Social + Injection:Social)

dds = DESeq(dds)

resultsNames(dds)
 [1] &quot;Intercept&quot;            &quot;ind.n_S2_vs_S1&quot;       &quot;Region_NS_vs_HY&quot;     
 [4] &quot;Region_TN_vs_HY&quot;      &quot;Injection_S_vs_L&quot;     &quot;Social_KF_vs_ISO&quot;    
 [7] &quot;Social_KFC_vs_ISO&quot;    &quot;Social_NF_vs_ISO&quot;     &quot;ind.nS2.RegionNS&quot;    
[10] &quot;ind.nS2.RegionTN&quot;     &quot;InjectionS.SocialKF&quot;  &quot;InjectionS.SocialKFC&quot;
[13] &quot;InjectionS.SocialNF&quot; 

The terms you need are &quot;InjectionS.SocialKF&quot;,&quot;InjectionS.SocialKFC&quot;, &quot;InjectionS.SocialNF&quot;, and you can look at each of them:
head(results(dds,name=&quot;InjectionS.SocialNF&quot;))
log2 fold change (MLE): InjectionS.SocialNF 
Wald test p-value: InjectionS.SocialNF 
DataFrame with 6 rows and 6 columns
              baseMean     log2FoldChange             lfcSE               stat
             &lt;numeric&gt;          &lt;numeric&gt;         &lt;numeric&gt;          &lt;numeric&gt;
gene1  9.9811166787259   1.25304112986447 0.819806376919295   1.52845984752303
gene2 30.3449455820337 0.0329442893152027 0.705199688255367 0.0467162562092241
gene3 3.83223545055379    1.0281136369045  1.64095596190233  0.626533350543196
gene4  11.232305747171  0.595738624408923   0.8243883031544  0.722643227868976
gene5 6.70950627004097  0.756449993378065   1.0631622863378  0.711509430967263
gene6 26.1431134888287 -0.854784518963918 0.625714541243558  -1.36609342219393
                 pvalue              padj
              &lt;numeric&gt;         &lt;numeric&gt;
gene1 0.126398405431826 0.978671002658464
gene2 0.962739373909937 0.999897888026606
gene3 0.530965168963838 0.978671002658464
gene4 0.469899103018657 0.978671002658464
gene5 0.476768608734069 0.978671002658464
gene6 0.171909642630577 0.978671002658464

As mentioned, you can do a LRT if you want to test all the Injection:Social term interactions terms at one go, that is, the null hypothesis is that all of them are zero:
dds = nbinomLRT(dds,reduced=~ ind.n*Region + Injection + Social)
results(dds)

Usually the individual terms are more intuitively than testing all of them are zero, but you might have a special need for this.