Urban economics is full of models that deal with land use transitions. But I think that may not be quite what you are looking for. Is it that you are looking for a model that suggests that the transition could be relatively sudden? So the transition hangs up for a time and then breaks through suddenly. Is this a tipping point that you are looking for? Alternatively, you might be focused on filtering-up rather than the more common filtering-down.

My view of the question of the question is the following

- first you have to define gentrification

- let us suppose that gentrification is the tendency to attract richer inhabitants

- for me this cannot be describe and a fortiori predicted by a model

-what I have constated in various continent is if a a group of some people tend to feel comfortable in a neighborhoud, they improve naturally their quality of livig This can attract wealthier residents and by a cumulative process create a gentrified  neighbourhood . A reason for the the begin of this process of gentrification is currently unknown for me. Mightbe transport, scenery, school,.... 

To clear up what I am trying to do:

I define gentrification as an influx of class (measured by educational attainment) as well as rising real estate value (measured by an increase in median home value) into previously low income and cheap housing neighborhoods. After finding these neughbirhoods (in my case the census tracts of nyc) I am using a logistic regression to find out which census variables are most likely to occur in gentrified neighborhoods to attempt to predict the process. The only predictive model I have seen so far Is by Melchert & Naroff (1987). I am trying to replicate this, with other variables and in a modern setting. 

What I am looking for is similar models that predict gentrification in a numeric way. Or if unavailable, other prediction methods.

For me (strictly personal)

educational attainment is very difficult to define and a question of personal choice, for example there is in Paris a school named "ecole du Louvre" where you get  some insights of what you can find in the Louvre museum. This ecole is prestigious but you can't earn a lot of money with this school. This three years curriculum  leads you to a degree equivalent to american college degree (in the states a college degree is equivalent to a three years degree at the university in France because we finish high school one year after the american degree). All the american college degree are not equivalent (the French higher education is rather complex). If you have the equivalent of a college degree in the prestigious "Ecole du Louvre" you will look for a neighborhood which appear nice to you but you won't have the money to afford a pricey neighborhood.Conversely somebody by chance and entrepreneurship spirit can earn a lot of money and live almost where he/she wish. What is the educational level of Bill Gates ?

regarding real estate value. This is simply non measurable. Micro market. In France, most of the scholars use the "perval" data base which provide the prices of some recent transactions. Interpolation with a so called "price of housing market surface" leads simply to insanity. I am not sure you have better in the US.  

Actually in the USA there is a lot of data available at the census tract level, which is a very small neighborhood area, containing on average 4000 people. As educational attainment I defined all Persian 25 and up with at least 4 years of college. I have identified 131 census tracts which have gentrified with if:

1) their median home value as well as their median household income were below the median of the city. These tracts are eligible to gentrify. 

2) out of these tracts, if the level of educational attainment as well as the median home value (inflation adjusted) rose in the top third percentile, I considered them to be gentrified.

in the next step, I used a logistic regression with a binary dependent variable (gentrified yes or no) with lots of different Socioeconomic variables, such as income, race, housing stock etc. unfortunately the model was not very useful to predict gentrification as it shows that these variables are all not good to predict it. I guess there actually might be no way to predict the process, or maybe i should use other variables.

What do you want to do with your model ?

a master dissertation, a PHD dissertation, a paaer (in which review? I think what you have is sufficient for a master's degree, but if you wish to go further I think you have to clarify the question of race, which is according with what i remember a choice.

Secondly, You have to consider that a "ghetto" can be a poor neighborhood (e;G; the black part of the municipality and what is called an "enclave" a diverse and vibrant  neighborhood e;g; the numerous chinese quarter  everywhere in the world.

Finally be carefull when using log (i have no time to explain)

What I could suggest is to have a qualitative approach. What are the neighborhood who have seen more dramatic increase in median home value ? Among them what are the neighbourhood who have seen a change in the nature of the residents. And finally what kind of gentrification was at play. (maybe they are various kind of gentrification) and finaly you conclude with some hypothesis on the way a neighborhood can gentrify. 

That is my point of view but I understand that you might have others.

All the best

So what I now understand is that what you want is simply an empirical model that could be used to predict gentrification. You have a large number of neighborhoods that have undergone gentrification. I have a suggestion for a method that might be of use for some of those neighborhoods, the ones in which the "gentry" have expanded from a contiguous neighborhood. The model that I suggest is to compare the price of housing in the to-be gentrified neighborhood (TBG) with the price on the periphery or boundary of the previously gentrified neighborhood (PG). When the price at the boundary of the PG exceeds the price in the TBG by an amount equal to the cost of converting the housing in TBG to gentrified housing, then the gentrification occurs.

First, let me suggest  a brief reading about boundary effects in another context (the context of zoning between residential and commercial activity). I assume that you can think of residential as the PG neighborhood and commercial as the TBG neighborhood.

https://www.researchgate.net/publication/265426821_The_Value_of_Zoning

Second, let me suggest that you estimate prices using hedonics. This is not so difficult to do and you need not go "insane" in the process. You might have a neighborhood variable that you interact with time. See if the coefficient on that variable reaches a common magnitude as you do this again and again. If so, you may have found a predictive indicator of gentrification.

It might be possible to do this sort of thing in one fell swoop by using event time across the various neighborhoods you have identified. For inspiration, let me suggest the following:

https://www.researchgate.net/publication/227638888_The_Effect_of_Group_Homes_on_Neighborhood_Property_Values

Article The Value of Zoning

Article The Effect of Group Homes on Neighborhood Property Values

Interesting, do you read French Peter ? we had a PHD dissertation in Lyon on hedonic model applied to some partss of  Lyon. The Guy is now professor at the university of Reims. Two apartments with the same address might have very different prices (sun light, view, ettc. I am not sure he took the time to translate his dissertation in English. Maybe what you could estimate is the price of he land, I tend to believe that there is in America a strong tendency to have ethnically segregated communities. So urban space is clearly divided, If you cross one street, the price of land and the "classification"  of the inhabitants might differ to a large extent.

Dominique, although I had to pass an exam in French, that was about 50 years ago. How I passed it I'll never know. Occasionally, I can pick out a word or a phrase, but I am really hopeless. What I can do is to run any document through google translate. Bingo. or I should say, voila. We are all multilingual today.

Yes, there are segregated neighborhoods in the USA. Racial segregation is only the beginning, there is segregation by income, ethnic origin, age, religion, etc. Is this not the case everywhere? Yes, neighborhood matters regarding price. But it is pretty easy to capture that in hedonics. I have my vays, so to speak, to estimate the price surface in an urban setting nonparametrically . . . and I'm not talking about a dummy variable for each neighborhood. You might find the following interesting:

https://www.researchgate.net/publication/46552003_Estimating_a_Price_Surface_for_Vacant_Land_in_an_Urban_Area

Peter

Article Estimating a Price Surface for Vacant Land in an Urban Area