The stimulus–response model is a
conceptual framework
A conceptual framework is an analytical tool with several variations and contexts. It can be applied in different categories of work where an overall picture is needed. It is used to make conceptual distinctions and organize ideas. Strong concept ...
in psychology that describes how individuals react to external
stimuli
A stimulus is something that causes a physiological response. It may refer to:
*Stimulation
**Stimulus (physiology), something external that influences an activity
**Stimulus (psychology), a concept in behaviorism and perception
*Stimulus (economi ...
. According to this model, an external stimulus triggers a reaction in an organism, often without the need for conscious thought. This model emphasizes the mechanistic aspects of behavior, suggesting that behavior can often be predicted and controlled by understanding and manipulating the stimuli that trigger responses.
Fields of application
Stimulus–response models are applied in international relations,
psychology
Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...
,
risk assessment
Risk assessment is a process for identifying hazards, potential (future) events which may negatively impact on individuals, assets, and/or the environment because of those hazards, their likelihood and consequences, and actions which can mitigate ...
,
neuroscience
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...
,
neurally-inspired system design,
and many other fields.
Pharmacological
dose response relationships are an application of stimulus-response models.
Another field this model can be applied to is psychological problems/disorders such as
Tourette syndrome
Tourette syndrome (TS), or simply Tourette's, is a common neurodevelopmental disorder that begins in childhood or adolescence. It is characterized by multiple movement (motor) tics and at least one vocal (phonic) tic. Common tics are blinkin ...
. Research shows Gilles de la Tourette syndrome (GTS) can be characterized by enhanced cognitive functions related to creating, modifying and maintaining connections between stimuli and responses (S‐R links). Specifically, two areas, procedural sequence learning and, as a novel finding, also event file binding, show converging evidence of hyperfunctioning in GTS.
Previous research on E-learning has proven that studying online can be even more daunting for lecturers and students who suddenly change their learning patterns from the classrooms to the virtual ones. This is mainly because the suddenness of this change makes it difficult for lecturers to fully prepare to lecture in the virtual learning environment. In light of the above-mentioned facts, this research proposes a novel model and integrates flow theory into the theory of technology acceptance model (TAM), based on stimulus-organism-response (S-O-R) theory, the SOR model has been widely used in previous studies of online customer behavior, and the model theory includes three components: stimulus, organism, and response. Assuming that stimuli contained in the external environment cause people to change, which affects their behavior.
Mathematical formulation
The object of a stimulus–response model is to establish a mathematical function that describes the relation ''f'' between the stimulus ''x'' and the
expected value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...
(or other measure of location) of the response ''Y'':
[Meyer, A. F., Williamson, R. S., Linden, J. F., & Sahani, M. (2017). Models of neuronal stimulus-response functions: elaboration, estimation, and evaluation. ''Frontiers in systems neuroscience'', 10, 109.]
:
A common simplification assumed for such functions is linear, thus we expect to see a relationship like
:
Statistical theory
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics.
The theory covers approaches to statistical-decision problems and to statistica ...
for
linear model
In statistics, the term linear model refers to any model which assumes linearity in the system. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, t ...
s has been well developed for more than fifty years, and a standard form of analysis called
linear regression
In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...
has been developed.
Bounded response functions
Since many types of response have inherent physical limitations (e.g. minimal maximal muscle contraction), it is often applicable to use a bounded function (such as the
logistic function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation
f(x) = \frac
where
The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L.
...
) to model the response. Similarly, a linear response function may be unrealistic as it would imply arbitrarily large responses. For binary dependent variables, statistical analysis with regression methods such as the
probit model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from ''probability'' + ''unit''. The purpose of the model is to es ...
or
logit model
In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations.
Mathematically, the logit is the ...
, or other methods such as the Spearman–Kärber method.
Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the stimulus-response relationship.
One example of a logit model for the probability of a response to the real input (stimulus)
, (
) is
:
where
are the parameters of the function.
Conversely, a
Probit model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from ''probability'' + ''unit''. The purpose of the model is to es ...
would be of the form
:
where
is the
cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x.
Ever ...
of the
normal distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is
f(x) = \frac ...
.
Hill equation
In
biochemistry
Biochemistry, or biological chemistry, is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology, a ...
and
pharmacology
Pharmacology is the science of drugs and medications, including a substance's origin, composition, pharmacokinetics, pharmacodynamics, therapeutic use, and toxicology. More specifically, it is the study of the interactions that occur betwee ...
, the
Hill equation refers to two closely related equations, one of which describes the response (the physiological output of the system, such as muscle contraction) to
Drug
A drug is any chemical substance other than a nutrient or an essential dietary ingredient, which, when administered to a living organism, produces a biological effect. Consumption of drugs can be via insufflation (medicine), inhalation, drug i ...
or
Toxin
A toxin is a naturally occurring poison produced by metabolic activities of living cells or organisms. They occur especially as proteins, often conjugated. The term was first used by organic chemist Ludwig Brieger (1849–1919), derived ...
, as a function of the drug's
concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...
.
The Hill equation is important in the construction of
dose-response curves. The Hill equation is the following formula, where
is the magnitude of the response,
/chem> is the drug concentration (or equivalently, stimulus intensity), is the drug concentration that produces a half-maximal response and is the Hill coefficient.
:
[
The Hill equation rearranges to a logistic function with respect to the logarithm of the dose (similar to a logit model).
]
Founder of the Model
Ivan Pavlov
Pavlov Pavlov (or its variant Pavliv) may refer to:
People
*Pavlov (surname) (fem. ''Pavlova''), a common Bulgarian and Russian last name
*Ivan Pavlov, Russian physiologist famous for his experiments in classical conditioning
Places Czech Republic
*Pavlo ...
started studying the digestive system in dogs by performing chronic implants of fistulas in the stomach, by which he was able to show with extreme clarity that the nervous system plays a dominant role in the regulation of the digestive process. Experiments on digestion led to the development of the first experimental model of learning, in which a neutral stimulus acquires the capacity to evoke a specific response further to repeated pairing with another stimulus that evokes the response.
Edward Thorndike
Thorndike, who proposed the model, believed that learning stemmed from stimulus and response. Pavlov popularized and revolutionized the theory though by experimenting on the dogs.
References
Further reading
*
Behavioral concepts
Psychological models
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