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→Moderated mediation
==Moderated mediation==
==Moderated mediation==
Mediation and [[moderation (statistics)|moderation]] can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.
Mediation and [[moderation (statistics)|moderation]] can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.
[[Moderated mediation]] is when the effect of the treatment ''A'' on the mediator and/or the partial effect ''B'' on the dependent variable depend in turn on levels of another variable (moderator). Essentially, in moderated mediation, mediation is first established, and then one investigates if the mediation effect that describes the relationship between the independent variable and dependent variable is moderated by different levels of another variable (i.e., a moderator). This definition has been outlined by Muller, Judd, and Yzerbyt (2005)<ref name="Muller">{{cite journal | last1 = Muller | first1 = D. | last2 = Judd | first2 = C. M. | last3 = Yzerbyt | first3 = V. Y. | year = 2005 | title = When moderation is mediated and mediation is moderated | journal = Journal of Personality and Social Psychology | volume = 89 | issue = 6| pages = 852–863 | doi = 10.1037/0022-3514.89.6.852 | pmid = 16393020 }}</ref> and Preacher, Rucker, and Hayes (2007).<ref name="Preacher">Preacher, K. J., Rucker, D. D. & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Strategies, methods, and prescriptions. Multivariate Behavioral Research, 42, 185–227.</ref>
[[Moderated mediation]] is when the effect of the treatment ''A'' on the mediator and/or the partial effect ''B'' on the dependent variable depend in turn on levels of another variable (moderator). Essentially, in moderated mediation, mediation is first established, and then one investigates if the mediation effect that describes the relationship between the independent variable and dependent variable is moderated by different levels of another variable (i.e., a moderator). This definition has been outlined by Muller, Judd, and Yzerbyt (2005)<ref name="Muller">{{cite journal | last1 = Muller | first1 = D. | last2 = Judd | first2 = C. M. | last3 = Yzerbyt | first3 = V. Y. | year = 2005 | title = When moderation is mediated and mediation is moderated | journal = Journal of Personality and Social Psychology | volume = 89 | issue = 6| pages = 852–863 | doi = 10.1037/0022-3514.89.6.852 | pmid = 16393020 }}</ref> and Preacher, Rucker, and Hayes (2007).<ref name="Preacher">Preacher, K. J., Rucker, D. D. & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Strategies, methods, and prescriptions. Multivariate Behavioral Research, 42, 185–227.</ref>
===Models of moderated mediation===
===Models of moderated mediation===
There are five possible models of moderated mediation, as illustrated in the diagrams below.<ref name="Muller" />
There are five possible models of moderated mediation, as illustrated in the diagrams below.<ref name="Muller" />
# In the first model the independent variable also moderates the relationship between the mediator and the dependent variable.
# In the first model the independent variable also moderates the relationship between the mediator and the dependent variable.
# The second possible model of moderated mediation involves a new variable which moderates the relationship between the independent variable and the mediator (the ''A'' path).
# The second possible model of moderated mediation involves a new variable which moderates the relationship between the independent variable and the mediator (the ''A'' path).
# The third model of moderated mediation involves a new moderator variable which moderates the relationship between the mediator and the dependent variable (the ''B'' path).
# The third model of moderated mediation involves a new moderator variable which moderates the relationship between the mediator and the dependent variable (the ''B'' path).
# Moderated mediation can also occur when one moderating variable affects both the relationship between the independent variable and the mediator (the ''A'' path) and the relationship between the mediator and the dependent variable (the ''B'' path).
# Moderated mediation can also occur when one moderating variable affects both the relationship between the independent variable and the mediator (the ''A'' path) and the relationship between the mediator and the dependent variable (the ''B'' path).
# The fifth and final possible model of moderated mediation involves two new moderator variables, one moderating the ''A'' path and the other moderating the ''B'' path.
# The fifth and final possible model of moderated mediation involves two new moderator variables, one moderating the ''A'' path and the other moderating the ''B'' path.
{|
{|
| [[File:Mediated moderation model 1.png|centre|thumb|
| [[File:Mediated moderation model 1.png|centre|thumb|
First option: independent variable moderates the ''B'' path.]]
First option: independent variable moderates the ''B'' path.]]
| [[File:Mediated moderation model 2.png|centre|thumb|
| [[File:Mediated moderation model 2.png|centre|thumb|
Second option: fourth variable moderates the ''A'' path.]]
Second option: fourth variable moderates the ''A'' path.]]
| [[File:Mediated moderation model 3.png|centre|thumb|
| [[File:Mediated moderation model 3.png|centre|thumb|
Third option: fourth variable moderates the ''B'' path.]]
Third option: fourth variable moderates the ''B'' path.]]
| [[File:Mediated moderation model 4.png|centre|thumb|
| [[File:Mediated moderation model 4.png|centre|thumb|
Fourth option: fourth variable moderates both the ''A'' path and the ''B'' path.]]
Fourth option: fourth variable moderates both the ''A'' path and the ''B'' path.]]
| [[File:Mediated moderation model 5.png|centre|thumb|
| [[File:Mediated moderation model 5.png|centre|thumb|
Fifth option: fourth variable moderates the ''A'' path and a fifth variable moderates the ''B'' path.]]
Fifth option: fourth variable moderates the ''A'' path and a fifth variable moderates the ''B'' path.]]
|}
|}
==Mediated moderation==
==Mediated moderation==