Which analysis for whether more likely to give response matching stimuli than not? This is probably incredibly basic but I'm a bit lost. What analysis would you suggest to identify whether participants are more likely to make a choice (out of 4 categories) which matches the preceding stimuli (one out of the same 4 categories) than a choice that does not match?
This is basically the kind of thing I'm working with
Stimuli  Choice     Match
  a         a         1
  c         b         0
  b         d         0
  a         c         0
  c         c         1
  d         d         1
  d         a         0

Essentially, I just want to know whether the cues influences participants choice, however I do not have data for baseline choices and I'm not sure that it would make sense to use any of the stimuli as a baseline category.

Ok if you have not assigned the stimulus at random then you can still model the problem using a Multinomial distribution:
$y_{i}∼Multinomial()$
where $y_{i}$ is the vector of outcomes each time the particpant chooses one of the {a,b,c,d}. For example, in your example dataset $y_{1} = [1,0,0,0]$
where the partcipant chose "a" getting 1 and the other elements zero. Then we can model the probability of participant $i$ choosing $j$ as:
$
\theta_{i,j}=\frac{e^{\beta X_{i} }}{\sum_{j} e^{\beta X_{i} }}
$
Where $X_{i}$ is the vector of stimulus and $\beta$ is its effect. For example, if you give the 1st participant "b" as the stimuli then you have $X_{1} = [0,1,0,0]$. You can fit this model and estimate the $\beta$ to see if it's zero meaning no effect by the stimulus on the choices or a significant effect. You can fit this model in R Stan using a Bayesian framework like this:
rm(list = ls())
library(tidyverse)
library(rstan)

#Simulating 200 observations
n = 200

#Creating the stimulus matrix which is unbalanced 
stimuli_matrix = matrix(NA, ncol = 4, nrow = n)
set.seed(123)
for(i in 1:n){
  samp = rmultinom(1, 1, prob = c(0,0.5,0.5,0))
  stimuli_matrix[i,] = as.vector(samp)
}
colnames(stimuli_matrix) <- c("A", "B", "C", "D")

beta = 5 #Effect of stimulus

Y = matrix(NA, ncol = 4, nrow = n)
for(i in 1:n){
  V.A = 0.25 + beta* stimuli_matrix[i,1]
  V.B = 0.25 + beta* stimuli_matrix[i,2]
  V.C = 0.25 + beta* stimuli_matrix[i,3]
  V.D = 0.25 + beta* stimuli_matrix[i,4]
  probs = c(V.A, V.B, V.C, V.D)
  probs = exp(probs)/sum(exp(probs)) 
  samp = rmultinom(1, 1, prob = probs)
  Y[i,] = as.vector(samp)
}

colnames(Y) = c("Y.A", "Y.B", "Y.C", "Y.D")

df = data.frame(cbind(Y, stimuli_matrix))

# Fitting the model
model_code = "
data{
int N;
int quadrants[N, 4];
matrix[N, 4] X;
}
parameters{
  real beta;
  vector[4] intercept;
}
transformed parameters{
  vector[N] theta_a = intercept[1] + X[,1]*beta;
  vector[N] theta_b = intercept[2] + X[,2]*beta;
  vector[N] theta_c = intercept[3] + X[,3]*beta;
  vector[N] theta_d = intercept[4] + X[,4]*beta;
  matrix[4, N]  theta;
  
  for(i in 1:N){
    theta[:, i] = softmax([theta_a[i], theta_b[i], theta_c[i], theta_d[i]]');
  }

}
model{

//Priors
  beta ~ normal(0,100);
  
  for(i in 1:4){
  intercept[i] ~ std_normal();
  }
  
//Likelihood
  for(i in 1:N){
  quadrants[i] ~ multinomial(theta[:,i]);
  }
}
"

model_data = list(
  N = nrow(df),
  quadrants = df %>% select(Y.A, Y.B, Y.C, Y.D) %>% as.matrix(),
  X = df[,5:8]
)


stan_run <- stan(
  data = model_data,
  model_code = model_code
)

In this example that I created, the stimuli has a significant effect on the choices and it's correctly estimated by the model:
print(stan_run, pars = "beta")


> print(stan_run, pars = "beta")
Inference for Stan model: cde133b8626006f7ba99d226760af33f.
4 chains, each with iter=2000; warmup=1000; thin=1; 
post-warmup draws per chain=1000, total post-warmup draws=4000.

     mean se_mean   sd 2.5%  25%  50%  75% 97.5% n_eff Rhat
beta 5.06    0.02 0.71 3.81 4.56 5.01 5.51  6.59  2240    1

Samples were drawn using NUTS(diag_e) at Mon Oct 25 23:25:03 2021.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at 
convergence, Rhat=1).

