PSR-GLMM/R User Guide (README)

This repository provides example workflows and documentation for genome-wide association studies (GWAS) and QTL mapping of non-normally distributed traits, with a particular emphasis on the Pseudo-Response (PSR) method.

The PSR-GLMM/R framework supports:

• Generalized Linear Model (GLM)
• Generalized Linear Mixed Model (GLMM)
• Population Parameters Previously Determined (P3D)
• Pseudo-Response (PSR) method
• Corresponding methods for ordinal traits

Supported trait types include:

• Binary
• Binomial
• Poisson
• Ordinal

For PSR, the framework supports both:

• Kinship-based random effects
• User-defined random design matrices

An optional switch is available to compute heritability (H²) and related genetic variance components.

1. Input File Description

1.1 Genotype file (gencsv)

CSV format. The first column is sample ID and is not used in computation. Remaining columns are genotype values.

Example:

Bin,F001,F002,F003,…
Bin1,-1,1,1,…
Bin2,-1,1,1,…
Bin3,-1,1,1,…

• Rows: SNPs
• Columns: individuals
• Genotype values are numeric (e.g., -1/0/1)

1.2 Phenotype file (phecsv)

CSV format. Each row corresponds to one individual.

Typical columns may include:

• Binary – binary trait (0/1)
• Poisson – count data
• Event – number of successes (binomial)
• Trial – number of trials (binomial)
• Ordinal – ordered categorical trait

1.3 Kinship matrix (kkcsv)

Required for GLMM / P3D / PSR (kinship mode).

• Square matrix of size n × n
• Individual order must match genotype and phenotype files
• Represents genetic relatedness among individuals

1.4 User-defined random design matrix (Z.csv)

Optional alternative to the kinship matrix for PSR.

• Dimensions: n × q
• Each column represents a random-effect factor
• Can include an optional ID column (ignored in computation)
• Used to construct random covariance as Z %*% t(Z)

1.5 Covariate file (cov.csv)

Optional fixed-effect covariates.

• Rows correspond to individuals
• First column may be ID (ignored)
• Remaining columns can be numeric or categorical
• Automatically expanded using model.matrix

2. Common Parameters

3. PSR Method Examples

3.1 The pseudo response method (PSR) for “binomial” trait

# ===== Mode A (Kinship K), no covariates =====
PSR(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = "data/kk.csv",
  zcsv   = NULL,
  covcsv = NULL,
  phename = "Event",
  phetype = "binomial",
  phenameother = "Trial",
  outpath = "PSR_A1_K_noCov_Binomial",
  h2 = FALSE,
  use_fixed   = FALSE,
  use_kinship = TRUE,
  use_randomZ = FALSE
)

# ===== Mode A (Kinship K), with covariates =====
PSR(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = "data/kk.csv",
  zcsv   = NULL,
  covcsv = "data/cov.csv",
  phename = "Event",
  phetype = "binomial",
  phenameother = "Trial",
  outpath = "PSR_A2_K_withCov_Binomial",
  h2 = FALSE,
  use_fixed   = TRUE,
  use_kinship = TRUE,
  use_randomZ = FALSE
)

# ===== Mode B (Random Z), no covariates =====
PSR(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = NULL,
  zcsv   = "data/Z.csv",
  covcsv = NULL,
  phename = "Event",
  phetype = "binomial",
  phenameother = "Trial",
  outpath = "PSR_B1_Z_noCov_Binomial",
  h2 = FALSE,
  use_fixed   = FALSE,
  use_kinship = FALSE,
  use_randomZ = TRUE
)

# ===== Mode B (Random Z), with covariates =====
PSR(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = NULL,
  zcsv   = "data/Z.csv",
  covcsv = "data/cov.csv",
  phename = "Event",
  phetype = "binomial",
  phenameother = "Trial",
  outpath = "PSR_B2_Z_withCov_Binomial",
  h2 = TRUE,   # example: turn on locus-level H2
  use_fixed   = TRUE,
  use_kinship = FALSE,
  use_randomZ = TRUE
)

3.2 The pseudo response method (PSR) for “binary” and “poisson” trait

PSR(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = "data/kk.csv",
  zcsv   = NULL,
  covcsv = NULL,
  phename = "Binary",
  phetype = "binary",
  phenameother = NULL,
  outpath = "PSR_A1_K_noCov_Binary",
  h2 = FALSE,
  use_fixed   = FALSE,
  use_kinship = TRUE,
  use_randomZ = FALSE
)

PSR(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = "data/kk.csv",
  zcsv   = NULL,
  covcsv = NULL,
  phename = "Poisson",
  phetype = "poisson",
  phenameother = NULL,
  outpath = "PSR_A1_K_noCov_Poisson",
  h2 = FALSE,
  use_fixed   = FALSE,
  use_kinship = TRUE,
  use_randomZ = FALSE
)

3.3 The pseudo response method (PSR) for “Ordinal” trait

# ===== Ordinal, Mode A1 (Kinship K), no covariates =====
PSR_ORDINAL(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = "data/kk.csv",
  zcsv   = NULL,
  covcsv = NULL,
  phename = "Ordinal",
  outpath = "PSR_Ordinal_A1_K_noCov",
  h2 = FALSE,
  use_fixed   = FALSE,
  use_kinship = TRUE,
  use_randomZ = FALSE
)

# ===== Ordinal, Mode A2 (Kinship K), with covariates =====
PSR_ORDINAL(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = "data/kk.csv",
  zcsv   = NULL,
  covcsv = "data/cov.csv",
  phename = "Ordinal",
  outpath = "PSR_Ordinal_A2_K_withCov",
  h2 = FALSE,
  use_fixed   = TRUE,
  use_kinship = TRUE,
  use_randomZ = FALSE
)

# ===== Ordinal, Mode B (Random Z), no covariates =====
PSR_ORDINAL(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = NULL,
  zcsv   = "data/Z.csv",
  covcsv = NULL,
  phename = "Ordinal",
  outpath = "PSR_Ordinal_B1_Z_noCov",
  h2 = TRUE,
  use_fixed   = FALSE,
  use_kinship = FALSE,
  use_randomZ = TRUE
)

# ===== Ordinal, Mode B (Random Z), with covariates =====
PSR_ORDINAL(
  gencsv = "data/IMF2-Genotypes-N.csv",
  phecsv = "data/IMF2-Phenotypes.csv",
  kkcsv  = NULL,
  zcsv   = "data/Z.csv",
  covcsv = "data/cov.csv",
  phename = "Ordinal",
  outpath = "PSR_Ordinal_B2_Z_withCov",
  h2 = TRUE,
  use_fixed   = TRUE,
  use_kinship = FALSE,
  use_randomZ = TRUE
)

4. Output Files

4.1 pseudo.csv

• id: Individual index
• y: Original phenotype
• p: Pseudo-response
• r: Working variance
• par: Estimated variance component

4.2 widedata.csv (PSR only)

• x*: Rotated fixed effects
• z*: Projected SNP values
• d: Eigenvalues

4.3 gwas.csv

• snp
• Variance
• effect
• StdErr
• wald
• p
• H2 (if enabled)

5. Software Availability

The PSR-GLMM/R software platform, together with user manuals, demonstration code, full source code, example datasets, and bibliographic references, is freely accessible at:

http://106.13.144.206/psrglmm/index.html