Hello, I am analyzing timecourse data of aging thymus samples. 29 samples, 11 different age groups. I am fitting splines for each gene and running LRT. Is there a more reliable way to tell how many degrees of freedom fit better (df = 4 vs df = 5), other than visually looking at the fitted splines for individual genes?

Also, are the LFC and lfcSE values at all useful for interpretation when fitting a non-linear model?

#The code I'm using
dds_df4 <- DESeqDataSetFromMatrix(countData = counts,
                                  colData = coldata,
                                  design = ~ ns(age, df = 4) + sex)

keep <- rowSums(counts(dds_df4 )) >= 10
dds_df4 <- dds_df4 [keep,]

dds_df4 <- DESeq(dds_df4 , test="LRT", reduced = ~ sex)

#(Thank you Mike)

sessionInfo( )
R version 4.3.0 (2023-04-21 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 11 x64 (build 22621)

Matrix products: default
locale:
[1] LC_COLLATE=English_United States.utf8  LC_CTYPE=English_United States.utf8   
[3] LC_MONETARY=English_United States.utf8 LC_NUMERIC=C                          
[5] LC_TIME=English_United States.utf8    

time zone: Europe/Berlin
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

loaded via a namespace (and not attached):
 [1] utf8_1.2.3                  generics_0.1.3              bitops_1.0-7               
 [4] DESeq2_1.40.1               lattice_0.21-8              digest_0.6.31              
 [7] magrittr_2.0.3              evaluate_0.21               grid_4.3.0                 
[10] fastmap_1.1.1               Matrix_1.5-4                GenomeInfoDb_1.36.0        
[13] fansi_1.0.4                 scales_1.2.1                codetools_0.2-19           
[16] cli_3.6.1                   rlang_1.1.1                 crayon_1.5.2               
[19] XVector_0.40.0              Biobase_2.60.0              munsell_0.5.0              
[22] yaml_2.3.7                  DelayedArray_0.26.3         S4Arrays_1.0.4             
[25] tools_4.3.0                 parallel_4.3.0              BiocParallel_1.34.2        
[28] dplyr_1.1.2                 colorspace_2.1-0            ggplot2_3.4.2              
[31] locfit_1.5-9.7              GenomeInfoDbData_1.2.10     SummarizedExperiment_1.30.2
[34] BiocGenerics_0.46.0         vctrs_0.6.2                 R6_2.5.1                   
[37] matrixStats_1.0.0           stats4_4.3.0                lifecycle_1.0.3            
[40] zlibbioc_1.46.0             S4Vectors_0.38.1            IRanges_2.34.0             
[43] pkgconfig_2.0.3             pillar_1.9.0                gtable_0.3.3               
[46] glue_1.6.2                  Rcpp_1.0.10                 xfun_0.39                  
[49] tibble_3.2.1                GenomicRanges_1.52.0        tidyselect_1.2.0           
[52] knitr_1.43                  rstudioapi_0.14             MatrixGenerics_1.12.2      
[55] htmltools_0.5.5             rmarkdown_2.22              compiler_4.3.0             
[58] RCurl_1.98-1.12

I usually use visual inspection.

Also, are the LFC and lfcSE values at all useful for interpretation when fitting a non-linear model?

For splines the LFC (the estimated coefficients) are not interpretable or meaningful.

I recently posted some code for helping to draw the resulting curves: